Voters in France will cast ballots on Sunday in the final round of snap legislative elections. The results could force President Emmanuel Macron to govern alongside far-right opponents or usher in chronic political instability weeks before the Paris Summer Olympics.

Mr. Macron called the elections for the 577-seat National Assembly, France’s lower and more prominent house of Parliament, last month in a risky gamble that appeared to have largely backfired after the first round of voting last week.

Most polls close at 6 p.m. local time on Sunday, or as late as 8 p.m. in larger cities. Nationwide seat projections by polling institutes, based on preliminary results, are expected just after 8 p.m. Official results will come in throughout the night.

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Hamas has softened its position in its latest Gaza cease-fire proposal but is sticking to a key demand that has been a major hurdle to a deal, according to two senior officials from countries involved in the negotiations.

That has dampened prospects for an imminent agreement, even as U.S. and Israeli officials have expressed optimism now that the talks are moving forward after weeks of deadlock.

Hamas presented a counterproposal on Wednesday. The two officials said that Hamas wanted international assurances that, once an initial truce kicks in, both sides will keep negotiating until they reach a final deal to end the war and free all of the hostages remaining in Gaza.

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Last month, Sophie-Laurence Roy, a conservative Paris lawyer with roots in Burgundy, decided to cross the political dividing line that defined postwar France and dedicate herself to a nationalist, far-right political movement that seems poised to dominate parliamentary elections on Sunday.

“I realized I would reproach myself for the rest of my life if I did not offer my services to the great movement of change that is the National Rally,” she said as she ate a sausage of pork intestines in a cafe in Chablis, the northern Burgundy town known for its fine white wine. “It was now or never.”

So, on June 9, Ms. Roy, 68, deserted her longtime center-right political family, the Republicans, who trace their beliefs to the wartime hero Charles de Gaulle, to support Marine Le Pen’s far-right party whose quasi-fascist roots lie with the collaborationist Vichy regime against which De Gaulle fought to liberate France.

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The victory of reformist candidate Masoud Pezeshkian in Iran’s presidential runoff signals a shift from the government of Ebrahim Raisi, a conservative Shiite Muslim cleric and the preceding president who was killed in a helicopter crash in May.

Mr. Pezeshkian, a 69-year-old cardiac surgeon who served as a lawmaker in previous reformist governments and as health minister, beat the hard-line conservative candidate Saeed Jalili in Friday’s runoff, the government announced on Saturday.

Here are the most important takeaways from the election.

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In an election upset in Iran, the reformist candidate who advocated moderate policies at home and improved relations with the West won the presidential runoff against a hard-line rival, according to results released by the interior ministry on Saturday.

The winner, Masoud Pezeshkian, a 69-year-old cardiac surgeon, got 16.3 million votes to defeat Saeed Jalili with 13.5 million votes. It was a blow to the conservative faction in Iran’s ruling establishment and a major victory for the relatively moderate reformist camp, which had been sidelined from politics for the past few years.

After polls closed at midnight, turnout stood at about 50 percent, roughly 10 percentage points higher than in the first round, with about 30.5 million ballots cast, according to the interior ministry.

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Prime Minister Keir Starmer of Britain will barely get his feet under the desk in 10 Downing Street before he flies to Washington this coming week to attend a NATO summit. A week after that, he will play host to 50 European leaders at a security meeting at Blenheim Palace, the birthplace of Winston Churchill.

It’s a crash course in global statecraft for Mr. Starmer, Britain’s first Labour prime minister in 14 years. But it will also give him the chance to project an image of Britain that is uncharacteristic in the post-Brexit era: a stable, conventional, center-left country amid a churning tide of politically unsettled allies.

In Washington, Mr. Starmer will encounter President Biden, who is resisting calls to abandon his race for re-election because of age-related decline. He will meet with President Emmanuel Macron, whose attempt to fend off the far right in France appears to have backfired, and with Chancellor Olaf Scholz of Germany, whose coalition has been weakened by the advance of the hard right in European Parliament elections.

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