PARIS — French voters dealt a sharp setback to the far-right National Front in regional elections on Sunday, depriving the party of victory in any of the country’s 13 regions, according to projections based on exit polls.

A week after the National Front came out on top in the first round of voting, France sent a far different message, with the party losing even in a northern region where its charismatic leader, Marine Le Pen, had been widely expected to win.

The projections also showed the National Front being defeated in another of its strongest areas, the south around Nice, where Ms. Le Pen’s 26-year-old niece, Marion Maréchal Le Pen, was on the ballot.

If confirmed when the vote count is completed, the results would confound expectations that the party, with its anti-immigrant, nativist message, was on the verge of an electoral breakthrough that could have added momentum and credibility to Ms. Le Pen’s hopes of winning the presidency in 2017.

The difference between the two Sundays: In the two main regions where the Front was thought to have had a chance of winning, the Socialist Party candidates dropped out, leaving the field clear for the mainstream conservative candidate.

“I salute the voters who responded to the appeal to block the far right,” said Prime Minister Manuel Valls of the governing Socialist party in a speech Sunday night, even as he warned that “the danger of the far right is not over, far from it.”

Polling had shown Ms. Le Pen’s party getting a strong boost in the aftermath of the terrorist attacks in Paris on Nov. 13 and from the suspicion that two of the attackers may have slipped into Europe with immigrants through Greece.

Early results Sunday had the governing Socialists winning four to five regions, with the mainstream conservative Republicans perhaps taking the rest, including Paris. In contrast to the verdict of commentators after the first round — that the poll-topping National Front had delivered a humiliating setback to the third-finishing Socialists — Sunday’s results could be seen as a boost to the governing party.

Recent polls have shown the Socialists’ leader, President François Hollande, advancing since the attacks last month — a period in which he has made a number of speeches aiming to reassure his shocked compatriots — perhaps putting him in a stronger position for re-election in 2017. His prime minister, Mr. Valls, appeared relieved as he thanked voters on Sunday night.

For weeks the National Front and its supporters had boasted that it was France’s leading party, and that the country had become a three-party system: left, right and — in the Front’s own terminology — nationalist.

But in the end, the results confirmed what an angry Ms. Le Pen herself declared in her concession speech: France is still a two-party country, those who are for the National Front, and those who are against it. “We really are in a bi-party system,” Ms. Le Pen told her supporters Sunday, “no longer right and left, but globalists and patriots, with the globalists working toward the dilution of France in a giant global magma.”

Ms. Le Pen made her presidential ambitions for 2017 clear: “This distinction will be what is fundamentally at stake in the huge political decision of the presidential elections.”

Yet in the northern region where she was on the ballot herself, Ms. Le Pen managed to take only about 42 percent of the vote, according to early projections, to the mainstream right’s 57 percent.

One expert on the Front, the political scientist Nicolas Lebourg, cited a recent poll showing that 60 percent of the French believe the party endangers French democracy. “They are very good in the first round, but they crash in the second,” Mr. Lebourg said Sunday night of the National Front.

Mainstream politicians appearing on television Sunday night all looked relieved in the wake of the Front’s resounding defeat. “I thank the voters who have protected our beautiful region,” said the right’s candidate in the north, Xavier Bertrand, who beat Ms. Le Pen.

In the first round of voting last week, the National Front came in first in six of the 13 regions, alarming France’s political and media establishment. With 28 percent of the vote, the far-right party achieved its best result ever, three percentage points better than in European elections last year, its previous best.

Fearing a Front takeover in two regions where Socialist candidates finished third — the north around Lille, where Ms. Le Pen was running, and the south around Nice, where her niece was the top candidate — the Socialist Party withdrew its candidates for the second round. The hope was that Socialist voters would then block the Front by voting for the mainstream conservative Republicans.

That hope apparently paid off.

In the eastern Alsace-Lorraine region, the Socialist incumbent ignored the calls from party headquarters in Paris. The incumbent, Jean-Pierre Masseret, refused to withdraw despite finishing a distant third, thus opening the way to a possible Front victory. In the end, though, Ms. Le Pen’s chief deputy — the party’s third strong candidate — was also defeated, according to the projections.