But, of course, the figure casting a shadow across the whole campaign is Marine Le Pen, the 48-year-old leader of the far-right National Front. Once the standard-bearer of a fringe extremist party, she is now at the forefront of a powerful, popular movement, eager to refashion France with an aggressively nationalist agenda. Thursday's shooting in Paris, for which the Islamic State has claimed responsibility, underscored how ripe France may be for Le Pen's hard-line message on immigration and Islam. Le Pen quickly pounced on the attack as proof of the need to shield France from “Islamist terrorism.”

My colleagues reported earlier in the week on one of the curious factors that distinguishes Le Pen's National Front from right-wing populists in Britain and the United States: The strong backing of millennials. One survey shows Le Pen winning 40 percent of the vote among those 18 to 24, a reflection of widespread youth disillusionment with the status quo.

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“We’ve been told our whole lives that everything is set. Free trade. Forgetting our borders. One currency for all of Europe. Nothing can change,” Gaëtan Dussausaye, the 23-year-old leader of the National Front’s youth wing, told my colleagues. “But young people don’t like this system. This system is a failure.”

“The National Front’s strength among millennials suggests the populist wave that’s unsettled the West may be more durable than many may assume,” wrote The Washington Post's Griff Witte and James McAuley. “Far from the last gasp of closed-society older voters who are demographically destined to be outnumbered by a rising tide of cosmopolitan youth, the populist insurgency could continue to build over years and decades if enough disenchanted young voters can be lured by the promise of something new.”

That something new hinges on a range of radical promises: the disbursing of new benefits to French citizens, a closing of borders, a retreat from NATO and the prospect of a referendum on France's membership in the European Union. A “Frexit,” though unlikely at the moment, could spell the end for the continental bloc.

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But while Le Pen and her supporters cast themselves as agents of change, they are saddled with the dark legacy of the past.

Le Pen's father, Jean-Marie Le Pen, became president of the National Front in 1972, shortly after it was founded. The party was “peopled by radical Catholics, monarchists, Vichy apologists, colonial nostalgics, neo-fascists and other marginal reactionaries,” as a recent article in the Guardian put it. “For the first decade of its existence, it distinguished itself mostly by its insignificance. Jean-Marie won 0.74 percent of the vote in the presidential election of 1974.”

The elder Le Pen — a believer in the “inequality of races” and an alleged participant in the torture of Algerian rebels during that country's war of independence against France — is an unrepentant extremist. To this day, he still is accused of “soft-core denial” of the Holocaust, as McAuley, The Post's Paris correspondent, reported earlier. The stigma of the National Front's connections to Nazi apologists, Vichy sympathizers and other extreme reactionaries enveloped Le Pen and his party for years.

Since assuming the mantle of leadership, Marine Le Pen has tried to distance herself from her father's incendiary rhetoric. “Our project is englobing; it's inclusive, not exclusive,” said Jean Messiha, a senior National Front official, in a combative interview with Al Jazeera last week. “You are talking about history. Don't take the Front National of the 70s as a reference.” If poll results are any indication, this strategy of “de-demonization” appears to have paid off.

But, at its core, the National Front remains a faction rooted in xenophobia and ultranationalist bigotry. Le Pen's inner circle still includes far-right rabble rousers who expressed forms of Hitler nostalgia in the past. Le Pen's candidacy has soared alongside growing anti-Muslim sentiment, stoked in part by the deadly spike in terrorist attacks in France that have claimed at least 230 lives in the past two years. Le Pen says she is against “Islamist globalization” — a neat amalgamation of two things she reviles — but wants to curtail the way Muslims practice their faith, seeks to limit immigrants' access to social services and education and is keen on ending birthright citizenship in France.

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But it's not just about Muslims.

Aymeric Chauprade, a former Le Pen adviser who fell out with the party over its attitude toward Israel, said ranking figures in Le Pen's camp remain genuinely “National Socialist.”

“They are anti-Semites, nostalgic for the Third Reich, violently anticapitalist, with a hatred for democracy,” he told the New York Times. “People think they’re marginal. But in fact, I discovered, she protects them. She supports them. They are at the heart of everything.”

Earlier this month, Le Pen infuriated Jewish groups and the Israeli government when she appeared to dismiss French responsibility for a 1942 operation in which 13,000 Jews in occupied Paris were rounded up, detained by local authorities and later shipped off to death camps.

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“Our children are taught that they have every reason to criticize, to see only the darkest historical aspects,” Le Pen said. “I want them to be proud to be French again.”

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In contrast, consider how Le Pen's main challenger, the centrist Macron, journeyed to Algeria in February and spoke of decades of brutal French colonization there as a “crime against humanity.” Macron faced a backlash for his remarks from outraged conservative opponents and suffered a brief dip in the polls.

If Le Pen ultimately defeats him, it may be a sign of the times and the anti-establishment mood sweeping the West. But it will also reflect the way in which a restless nation, uncertain about its future, is reckoning with its past.