SANARY-SUR-MER (FRANCE) — The National Front’s leafleteers are no longer spat upon. Its local candidate’s headquarters sit defiantly in a fraying Muslim neighbourhood. And last week, Ms Marine Le Pen, the party’s leader, packed thousands into a steamy meeting hall nearby for a pugnacious speech mocking “the system” and vowing victory in this spring’s French presidential election.

“There’s been a real evolution,” Mr Philippe Renault-Guillemet, the retired head of a small manufacturing company, said as he handed out National Front leaflets in the market on a recent day.

“A few years ago, they would insult us. It’s changed.”

It has long been accepted wisdom that Ms Le Pen and her far-right party can make it through the first round of the presidential voting on April 23, when she and four other candidates will be on the ballot, but that she will never capture the majority needed to win in a runoff in May.

But a visit to this south-eastern National Front stronghold suggests that Ms Le Pen may be succeeding in broadening her appeal to the point where a victory is more plausible, even if the odds are still stacked against her.

With a month to go, the signs are mixed. Many voters, particularly affluent ones, at markets here and farther up the coast betray a traditional distaste for the far-right party. Yet others once repelled by a party with a heritage rooted in France’s darkest political traditions — anti-Semitism, xenophobia and a penchant for the fist — are considering it.

“I’ve said several times I would do it, but I’ve never had the courage,” Mr Christian Pignol, a vendor of plants and vegetables at the Bandol market, said about voting for the National Front. “This time may be the good one.”

“It’s the fear of the unknown,” he continued, as several fellow vendors nodded. “People would like to try it, but they are afraid. But maybe it’s the solution. We’ve tried everything for 30, 40 years. We’d like to try it, but we’re also afraid.”

French politics are particularly volatile this election season. Traditional power centres — the governing Socialists and the centre-right Republicans — are in turmoil. Ms Le Pen’s chief rival, Mr Emmanuel Macron, is a youthful and untested politician running at the head of a new party.

Those uncertainties — and a nagging sense that mainstream parties have failed to offer solutions to France’s economic anaemia — have left the National Front better positioned than at any time in its 45-year history.

But if it is to win nationally, the party must do much better than even the 49 per cent support it won in this conservative Var department, home to three National Front mayors, in elections in 2015.

More critically, it must turn once-hostile areas of the country in Ms Le Pen’s favour and attract new kinds of voters — professionals and the upper and middle classes. Political analysts are sceptical.

Mr Frederic Boccaletti, the party’s leader in the Var, located in south-eastern France, knows what needs to be done. Last week, he and his fellow National Front activists gathered for a planning session in La Seyne-Sur-Mer, a working-class port town devastated by the closing of centuries-old naval shipyards nearly 20 years ago. Mr Boccaletti, who is running for Parliament, keeps his headquarters here.

“I’m telling you, you’ve got to go to the difficult neighbourhoods — it’s not what you think,” Mr Boccaletti told them, laughing slyly. “Our work has got to be in the areas that have resisted us most” — meaning the coast’s more affluent areas.

Ms Le Pen and her party still show little compunction over using tried-and-true National Front strategies that stoke racial fears. A wall in Mr Boccaletti’s tiny party headquarters is adorned with a poster showing a hand tearing down a star and crescent, a symbol of Islam, with the slogan “Here, We Are in France”. Another poster showed a veiled Muslim woman accompanied by the words “No to Islamism”.

When the beaming Ms Le Pen clambers onstage at her rallies, menacing chords give way to triumphant brassy blasts. At the more elaborate rallies, Wagnerian electric flame throwers dramatically cap her closing vows to “renew the ties of national solidarity”.

In Saint-Raphael, it was Ms Le Pen’s thrusts against the “mass immigration” and its supposed link to France’s mass unemployment that drew the loudest roars. “This is our country!” the crowd chanted.

“She’s going to send home the immigrants,” said Mr Jean Simon, a grizzled construction worker from Nice, who attended. “There’s way too much unemployment.”

Ms Le Pen is in the unusual position of seeming like a winner and a loser at the same time.

She is a winner because every French poll predicts she will come out on top in the first round. Four major candidates will be competing against her that day — two on the left, one in the centre and one on the right. None, alone, can beat her.

But she is a loser because those same polls all say she will be defeated by a hefty margin in the second round of voting on May 7, whoever her opponent is.

“I don’t think she will be elected President,” said Mr Joel Gombin of the University of Picardy Jules Verne, one of France’s leading experts on the Front. “But it’s not impossible any longer.’’

The ambiguous status of winner and loser gives her whole campaign — the tone of her voters, her activists, her top lieutenants and even Ms Le Pen herself — an uncertain feel, as if all are floating a few feet above reality.

Ms Muriel Fiol, a local doctor who was helping Mr Boccaletti run the meeting, predicted that the “glass ceiling was going to explode”.

“People don’t want this political class any more,” she said.

But Mr Boccaletti urged prudence. There was still some way to go, as attitudes of many locals showed.

Even if buoyed by the feeling that Ms Le Pen is a player for the first time, volunteers conceded that the going was “difficult”, as was sometimes shown by the reception at the colourful market in this fishing port of pastel houses on the Mediterranean.

Certainly, not all were convinced that Ms Le Pen had outrun the long shadow of her party’s ugly reputation.

“Sure, I took their leaflet,” Mr Bernard Cornet, a retired teacher, said, broadly grinning. “Only so that I could throw it into the trash straight away.” THE NEW YORK TIMES