France is among the world’s most storied welfare states, the historic province of the 35-hour workweek and, now, “the right to disconnect” from work emails after leaving the office.

For decades, the country has been home to one of Europe’s strongest Socialist parties, which managed to influence policy even when technically out of power. But as France prepares for its 2017 election — a contest widely expected to shape the course of a troubled Europe — a jarring reality has emerged.

Quite simply, the Socialists have almost no chance of winning, according to nearly every major public opinion poll. And they are increasingly unlikely to qualify for even the second and final round of the presidential election, to be held in early May.

As the power of the center-left wanes across the Western world — in the Europe of Brexit and in the United States of Donald Trump — it looks as though France may follow suit.

On Sunday, French voters went to the polls in the first round of an election to choose which one of seven candidates they want to lead the center-left come late April and early May. In first and second place came Benoît Hamon, a former education minister, and Manuel Valls, the former prime minister of François Hollande, France’s current Socialist president and the most unpopular president in the country’s modern history.

One of the two will be chosen in a second-round vote next Sunday.

After that, the climb to victory gets much steeper.

First is the threat from Emmanuel Macron, an increasingly popular former finance minister who defected from the current Socialist administration to launch an independent and more-centrist campaign.

Second is the specter of the ­center-right François Fillon and the rightist Marine Le Pen, both of whom are expected to make the final round of the presidential election in May.

For the first time, Le Pen has polled ahead of Fillon, suggesting what for decades has been unthinkable: that the National Front, France’s far-right populist party of xenophobia and economic protectionism, could actually win a national election.

The National Front, once a ­pariah party, has become the linchpin of a pan-European coalition of far-right parties. On Saturday, Le Pen spoke at a summit of other nationalist leaders in Koblenz, Germany — a gathering that also included Geert Wilders, the leader of the anti-Islam Dutch Freedom Party, and Frauke Petry, a joint leader of the Alternative for Germany party, one of whose other leaders drew headlines last week for attacking Holocaust atonement.

“In 2016, the Anglo-Saxon world woke up,” Le Pen said at the conference. In “2017, I am sure, the people of continental Europe will wake up.”

In France, Socialists have begun to worry that her prediction will come true. In the final days before Sunday’s vote, even some of the leftist candidates seemed to have considered their primary a fool’s errand in a changing country.

This was a point made by Jean-Luc Bennahmias, one of the virtually unknown candidates, in one of the contest’s televised debates. Before a reported 3 million viewers, Bennahmias acknowledged that he was a “little candidate” with whom few were familiar.

But, he added, so was everyone else on the stage, in the grand scheme of things. “There are no candidates here who have the floor on the big subjects,” he said.

Data suggests that he is correct. Apart from Le Pen and Fillon, the most recent opinion poll conducted by Le Monde newspaper and the Cevipof agency ranked all Socialist candidates behind the centrist Macron, a former investment banker, and even the far-left candidate Jean-Luc Mélenchon.

The reasons for the surprising demise of the Socialist Party in France are manifold.

For starters, Hollande is staggeringly unpopular. He has struggled with relatively high and constant unemployment and a wave of terrorist violence that has killed 230 in the past two years.

Hollande decided in December not to run for reelection. This is the first time in a primary that a ruling leftist party is not represented by its incumbent president.

But analysts see the fall of the Socialists as part of a deeper trend away from a perceived establishment, which in France has long been dominated by the center-left. The same dissatisfaction with the realities of an increasingly globalized economy that fueled much of the Brexit campaign — and the Trump campaign — has begun to see an enemy in the French left.

“There is a general crisis in social democracy,” said Gérard Grunberg, a renowned historian of the French left at Sciences Po in Paris. “And it’s become more and more difficult to show why it matters, what its values are, against the evolution of financial capitalism and globalization. What’s come back is anti-liberalism, reaction.”

In the throes of these significant external challenges, Grunberg said, there is virtually no unity on the center-left to sway voters away from the extremes on either end of the political spectrum. “The party is no longer a community,” he said.

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