“The S.N.C.F. faces attacks on its network every year, every month even,” said Julien Joly, a transportation expert at the Wavestone consulting firm, using the abbreviation for France’s national railway company.

He added: “But never in these proportions, and never in such a coordinated way. Unfortunately the network is so vast, you can’t ensure a 24-hour security presence everywhere.”

France has a very dense train network, with 28,000 kilometers of tracks (about 17,400 miles) used by 15,000 trains every day. Much of it is separate from the high-speed train network.

But the TGVs, as the high-speed trains are known, whisk thousands of passengers across the country daily, and are one of France’s most prized national infrastructures — a symbol of its technical know-how.

Arnaud Aymé, a transportation expert at the Sia Partners consulting firm, said that the infrastructure that was targeted — signal stations and cables — were often protected with alarms, cameras, fencing and barbed wire, and were not always easily accessible.

But train networks, because they are expansive but also limited by nature — a technical failure on one track creates an immediate bottleneck — are hard to make failproof.

“Railway networks are particularly open,” Mr. Aymé said, vulnerable to a fallen tree, an unlucky lightning strike on an electrical substation or a malicious act.

Any disruptions have “cascading effects,” he said. “Even if the network is repaired, it takes time for everything to get back in order,” he added.

Railway networks face thousands of criminal acts every year, experts say: People steal electrical cables to sell copper wire on the black market or carry out petty acts of vandalism.

But the level of coordinated and simultaneous sabotage that happened Friday is extremely rare, experts say. The S.N.C.F. said that it detected the arson around 4 a.m. and quickly intervened alongside firefighters and police.

French prosecutors have opened a criminal investigation. They say there is no doubt that the fires were intentionally set, but have said that it is too early to determine who the suspects are and what had motivated them.

It was also unclear if the aim was to disrupt the Olympics directly, or to merely to embarrass the French authorities as the country had large-scale international attention. Experts noted that sabotage on the Paris commuter lines — which are expected to ferry hundreds of thousands of Olympic visitors — would have been more directly devastating to the Games.

None of the targets are close to the French capital. The S.N.C.F. said that arsonists successfully targeted infrastructure in Courtalain, southwest of Paris; Pagny-sur-Moselle, to the east; and Croisilles, to the north. All are more than 100 kilometers (62 miles) from the French capital.

All the four main high-speed lines sprout out of Paris, connecting it to the rest of the country. Only one of the three was undisturbed on Friday after an arson attack was thwarted on the southern line leading to the French Alps and the Mediterranean, the S.N.C.F. said.

“Critical points were targeted, which shows that they knew enough about the network to know where to strike,” Gabriel Attal, France’s prime minister, told reporters after a crisis meeting on Friday.

The S.N.C.F. said that the suspected arsonists had cut and burned cables that are used for train signaling — each cable is split into dozens or even hundreds of fiber optic threads that have to be repaired, reconnected and tested.

The suspected arsonists targeted infrastructure right before the tracks split into two different directions, ensuring that two branches of the line, not just one, would be affected by the disruptions.

“The locations were particularly chosen to have more serious consequences,” Jean-Pierre Farandou, the president of the rail company, told reporters on Friday.

The fires, which were detected at about 4 a.m. on Friday, disrupted France’s Atlantic, North and East rail arteries, halting or slowing trains between Paris and major cities that are hosting some Olympic competitions, including Bordeaux, Marseille, Nice and Lille.

The outages also rippled to international services, including high-speed service involving Belgium and the Eurostar between London and Paris, with delays of as long as 75 minutes. Eurostar said in a statement that it would cancel 25 percent of its trains through Sunday.

The chief executive of S.N.C.F., Christophe Fanichet, warned that there would be delays of up to two hours on some long-distance lines. “We ask people please not to come to the station, because if you haven’t heard from us, your train won’t be running,” he said.

By midafternoon, some high-speed trains were running again after workers carried out emergency repairs. But S.N.C.F. said that traffic would remain disrupted in the coming days. France’s transportation minister, Patrice Vergriete, said authorities were “preparing themselves” for other potential attacks.

Despite the disruptions to long-distance trains, the Paris Metro was running fairly smoothly on Friday. Around two dozen Metro stations were being closed in the afternoon along the Seine, where a flotilla of boats will ferry 10,000 athletes to the Eiffel Tower. After the parade ends at around 11:30 p.m., two automated Metro lines will run all night long to clear crowds.

With some of Paris’s biggest train stations, including Montparnasse and Gare du Nord, crowded with stuck passengers, travelers looked to car rental companies or other transport alternatives. Uber said in a statement that it was ​​offering a 15 percent discount code for rides originating from all major train stations in France through Sunday night “to help people get where they need to, safely.” Other travelers turned to companies like FlixBus, which offered service to Bordeaux and Brittany.

On the Champs Elysees, which was closed off to traffic, hundreds of people biked or walked to their destinations.

But for the thousands of people stuck at train stations, the wait was agonizing.

Even before the opening ceremony, Olympians in rugby, soccer, handball and archery had begun competing this week, including some in cities across France. But with many trains canceled, it was unclear how they would get to Paris in time for the opening ceremony. Two trains carrying Olympic athletes to Paris on the Atlantic line were stopped hours before the opening ceremony, S.N.C.F. said.

Sorelle Maximillien was one of the lucky ones who had made it on Friday to Gare de Lyon, one of Paris’s largest train stations, from Saint-Étienne, a city in eastern France, despite a delay after the conductor announced that unidentified people had walked onto the tracks, disrupting service.

But her brother was stuck in Marseille after his train was canceled, with signs flashing in that station that service was likely to resume on Monday. Ms. Maximillien’s parents had traveled to Paris from Guadeloupe to celebrate the Olympics with family. “But now my son can’t come today because of the train problems — we hope we’ll see him soon,” said Arsène Maximillien, Sorelle’s father.

Here’s what we know about the attacks and the resulting disruptions:

Is this a terrorist attack?

That is not clear yet, but France’s prime minister, Gabriel Attal, has described the fires as “acts of sabotage that were carried out in a prepared and coordinated way.” The police and intelligence services are investigating these “criminal acts,” he added in a post on social media.

So far, evidence shared by the French authorities suggests that the attacks were planned and deliberate. The fires all broke out at the same time on Friday, around 4 a.m. local time, said Patrice Vergriete, France’s transportation minister.

Jean-Pierre Farandou, the head of France’s national rail company, S.N.C.F, described the repairs that the attacks have necessitated as “very meticulous work.” The fires were set in pipes that carry cabling necessary for signaling, and located on key bifurcation points on the rail, meant to maximize the damage, Mr. Farandou said.

The episode is bound to raise fears in a country already deeply scarred by terrorist attacks. In 2015, attackers linked to the Islamic State killed 130 people in and around Paris. Then, in 2016, an attacker drove a bus through a crowd celebrating Bastille Day in Nice, in southern France. Lone assailants have also carried out shootings and stabbings, including the grisly beheading of a teacher in 2021.

Security had already been rigorous ahead of the Games, and in the immediate aftermath of the attacks, a security perimeter in Paris has been further tightened.

How bad are the disruptions?

The attacks have brought France’s rail system to a near standstill, causing chaos during a particularly busy time. More than one million people were expected to travel on the national rail system this weekend, according to France’s rail company. Not only were travelers making their way to Paris for the Games, but many French citizens were trying to leave the city for summer vacations. Some said that they wanted to get away from Olympic crowds. The repair work, the rail company said, is likely to take all weekend.

The fires were set on three of France’s four high-speed national lines, the Atlantic, Northern and Eastern, according to S.N.C.F. Authorities responded to fire on the line between Paris and Lille, around the town of Arras, about 100 miles north of Paris, the capital. Another fire was reported on the connection between Le Mans and Paris, near Courtalain, a town about 90 miles southwest of Paris. The rail company said that it thwarted an attack on a route that connects Paris to southeast France.

The Eurostar, the high-speed rail service that connects several countries in Western Europe, said that its service to Paris had been delayed by at least 90 minutes. Around Paris, about two dozen Metro stations on the route to the location of the opening ceremony, on the Seine, were shut. Security concerns also affected other modes of transport. Authorities briefly ordered the evacuation of the EuroAirport Basel-Mulhouse-Freiburg, the French-Swiss airport near Basel, Switzerland, citing unspecified “safety reasons.”

How will this affect the Olympics?

The opening ceremony is expected to go ahead, but under heightened security. That increased security may make it harder for some visitors to reach Paris, even those using modes of transport not directly affected by the attacks.

The attacks have also cast a shadow over the start of the Games, dominating the public conversation and blighting the image of a country that had sought to project a sense of security over its hosting of the event.

The mood in the host city had already been tense, with tens of thousands of police officers, counterterrorism units and military personnel deployed to guard not only Olympic venues, but tourist sites, street corners and train stations. A section of the Seine had already been cordoned off on both banks.

At the Gare Montparnasse, travelers hunched over their phones looking for alternate routes out of the French capital. Children waited atop makeshift seats of suitcases. A slew of announcements played over the loudspeaker system. The words “act of malice” and “vandalism” echoed throughout the hall, doing little to quell the anxiety among travelers.

Some people at the Gare Montparnasse found their way to the rental car kiosks only to confront long lines of others who had the same idea.

At the Gare du Nord train station, about four miles northeast of Gare Montparnasse, Guillaume Du Pontavice stared in frustration at the departure board as each update pushed back his arrival time in Brussels, where he was supposed to surprise the groom at a bachelor party.

“Every two minutes, they add another 10-minute delay,” he said, with his bags on the floor between his legs. “I’d prefer them to tell me straight away that it’s canceled.”

A delayed train from Le Mans, in northwestern France, caused Océane Godemer and her friends to miss their original train to London.

“They got us on the next train for free, and it’s running as usual, so that’s OK,” she said as her friends finished eating breakfast. “But we’re still going to miss our visit to Buckingham Palace.”

The disruptions were also felt in London, where Eurostar, which operates trains to Paris, had delays of as long as 75 minutes. Eurostar said in a statement that it would cancel 25 percent of its trains through Sunday.

At St. Pancras International in London, travelers waited in long lines that stretched throughout the station.

Mary McCarthy, 65, started the day at 4 a.m. in West Cork, Ireland, driving to a nearby airport and flying to London to take the Eurostar to Paris. She was waiting for her daughter to join her and hoping her afternoon train to Paris was still running.

“If we can get there, we’ll be happy,” she said.

Paris was already grappling with the restrictions established by the heightened security measures for the Olympics, with about two dozen Metro stations closed.

“I guess the whole city is collapsing a little bit, so many streets are closed, all this security,” said Sofia Lascurain, whose Eurostar train to Bruges, Belgium, was delayed by at least an hour. “The city feels weird.”

Andrew Das and Dodai Stewart contributed reporting from Paris. Isabella Kwai contributed reporting from London.

The dragnet yielded some results. In central France, a man of Chechen origin was charged in May with the planning of an attack outside an Olympic soccer match in Saint-Étienne. Another man, a neo-Nazi sympathizer living in the Alsace region, was sentenced to two years in prison for publishing an explosives recipe online and for making threats.

This week, a 40-year-old Russian man was charged with working at the behest of a foreign power to “provoke hostilities” in France intending to destabilize the Olympic Games.

The police also did background checks on around one million people involved in the games, including security guards, stadium workers and volunteers, France’s interior minister, Gérald Darmanin, said earlier this week.

Of those, about 5,000 people were rejected because of their criminal records or flagged for “radicalization.”

Around 1,000 of them were suspected of foreign espionage, Mr. Darmanin said.

“These people, we thought it wouldn’t be a good thing for them to work in stadiums or accompany volunteers or the teams,” he said.