On the wall in the new presidential campaign offices of France’s Front National leader Marine Le Pen hangs a portrait of Hollywood tough guy Clint Eastwood. He might seem an odd choice of pinup for Europe’s biggest far-right, nationalist, anti-immigration party, but Le Pen admires Eastwood’s “bravery” in voting for Donald Trump in the US election last month. Dirty Harry, like Trump himself, has become something of a feel-good mascot for the French far-right’s battle for the leadership of the country. Instead of a gun, the ageing but still snarling Eastwood is pointing a blue rose, Le Pen’s new campaign symbol.

Trump’s US victory blew apart any notion of foregone electoral conclusions, leading Paris’s mainstream politicians to warn that the world’s next political earthquake could happen in France. Le Pen winning the French presidential election in five months’ time – something that had always been seen as impossible – would be the greatest shock in postwar European politics.

The panicked warnings carry an element of admission of defeat from France’s mainstream right and left parties. For years, they have shouted that the Front National is a dangerous, racist, xenophobic and Islamophobic party, yet they have been unable to stem its slow, but steady, rise. In fact, all the mainstream parties have borrowed Le Pen’s rhetoric on immigration and anti-terrorism in an attempt to compete. However, as Jean-Marie Le Pen – the party’s founder, a gruff ex-paratrooper and Marine’s father – is fond of saying: “Voters prefer the original to the copy.”

Le Pen with her romantic partner and political deputy Louis Aliot. Photograph: Liewig Christian/Corbis/Getty Images

Every poll currently indicates that Le Pen – running an anti-immigration campaign and warning of Islam’s dangers to France while promising a return of the nation-state and economic protectionism – will make it through to the presidential final round in May. However, the same polls show she cannot win because a barrage of tactical voting by people from all sides will keep her out.

Le Pen, though, says she feels “comforted” by Trump’s victory. She sees it, alongside Britain’s vote to leave the European Union, as the dawn of a new world order. For her, Trump is proof that the “political and media elite” can be put in their place, that establishment predictions can be proved wrong.

Front National voters can no longer be confined to a particular stereotype. They are not simply a pocket of working-class, former Communist voters in France’s northern rust belt or better-off, hard-right voters on the Côte d’Azur. Like Trump, Le Pen scores higher among those with lower levels of education, but that is not the only factor. Her reach has grown in areas of inequality; the further away a person lives from a railway station, the more chance they have of voting Front National. But the party has also expanded its reach to employees in private companies and now touches every stratum in society, from alpine villages to suburban towns. The party has won over the working class from the left and is making gains in the public sector, once hostile to the far right. More than half of the police and the military now vote Front National.

Front National voters are united “by a sense that they don’t feel represented by the workings of the current political system”, says Joël Gombin, a far-right expert and a politics professor at the University of Picardie Jules Verne. They are fed up with traditional parties who failed to protect them from the economic crisis and from what many see as the dangers of immigration and recent terrorist attacks.

François Fillon, another social conservative with a hardline approach to immigration, is Le Pen’s most likely barrier to the presidency. Photograph: Jean-Francois Monier/AFP/Getty Images

France remains under a state of emergency, fearing fresh attacks and their possible impact on the vote. The unpopular governing Socialist party has yet to choose its candidate, fearful of electoral wipeout, and the left is fragmented.

Le Pen’s slick new headquarters – located on one of Paris’s most expensive streets, a short walk from the presidential palace – are a sign of her growing confidence.

“Trump has given us so much hope,” smiles Bernard Bradland, 69, a Front National party worker from the outskirts of Paris as he cheers Le Pen at a party meeting after she had donned a cowboy hat to ride a horse around the ring at an equestrian show. (Riding horses, as Nicolas Sarkozy found when he pranced around in a checked cowboy shirt on a white horse in the Camargue, is a vote-winner.)

Bradland used to work in the mechanics business, where he says multinationals “swallowed up and spat out” small companies. To him, Trump and Le Pen stand for “the suffering citizens versus the oligarchy”. “The nation and the family is the foundation for everything,” he says. “You can’t live by opening borders; culture is not interchangeable. Globalisation is like sitting on your sofa and leaving the doors open, telling the people in the next building to come in and take what they want.”

How far the “Trump boost” will work for Le Pen remains to be seen. The Front National’s growth in the five years since Le Pen took over the leadership from her father has been unparalleled in the party’s history. In recent years, it has topped the polls in a series of local elections, leading it to claim the title, in electoral terms, of “the first party of France”. Its number of elected officials – from mayors to regional councillors and, for the first time, senators – has shot up. Is is now the No 1 party among French voters aged between 18 and 24, although this age bracket is also the most likely to abstain.

Even if Le Pen doesn’t win the presidency, the Front National could potentially increase its number of MPs from two to anything up to 60 in the parliamentary elections that will follow in June, which would give it significant influence in parliament.

Le Pen’s public drive to “detoxify” and broaden the appeal of the xenophobic movement is the latest of many public relations drives in the party’s 45-year history to attempt to make it more palatable to voters. But while she has moved – on the surface at least – to rid it of the old jack-booted imagery and antisemitic overtones, she has played a tricky balancing act of clinging to its most radical ideas, including the notion of “France for the French” – where native French people would be prioritised for benefits, housing and jobs – and portraying Islam as the biggest threat to the country.

The climate in France has worked in her favour. In a country where more than 230 people have been killed in terrorist attacks in a little more than 18 months, and where more than 3 million people are jobless after decades of mass unemployment, there is a growing audience for her hard line on security and national identity and her targeting of Islam and immigration.

Two Front National supporters wearing T-shirts emblazoned with the first line of the French National anthem. Photograph: Francois Nascimbeni/AFP/Getty Images

However, as Le Pen is acutely aware, many voters are still afraid of the party. “Only a third of people think that the Front National is capable of governing France and Le Pen being president,” the political scientist and far-right expert Nonna Mayer has observed.

Whether Trump’s win can boost Le Pen’s credibility by association is uncertain. She shares some of his views – an anti-immigration stance, a commitment to economic protectionism, an anti-establishment ambition to rise against the mainstream political class and a putative desire to “drain the swamp” of the elite, lobbyists and special interests. Like Trump, she is pro-Putin.

But there are key differences. Trump was the candidate for the US Republican party, a mainstream party. Le Pen leads an outsider movement. Trump is a political novice. Le Pen was born into a political dynasty, the youngest of three blond sisters who from a young age were wheeled out by their father to symbolise the true French nation. She has been in elected politics for almost 20 years. Trump made outrageous pronouncements at rallies, subverting his party’s policy lines and raging against political correctness. Le Pen has carefully toned down parts of her rhetoric so she can shift her party into the mainstream. It was her father who used to play the Trump role of shouty, protest outrage, but his daughter has put an end to that, evicting him from the party last year after a dramatic feud for his repeated belittling of the Holocaust. “Le Pen is an outsider trying to appropriate mainstream codes, Trump is an insider trying to present himself as an outsider,” says Gombin.

The crucial difference between Trump and Le Pen is their respective electoral systems. The French president – who holds the greatest amount of executive power in any western democracy – is directly elected in a two-round vote. Two candidates face each other in the final round and the winner needs to take more than 50% of the popular vote. Trump, who won under the US’s unique electoral college system, took about 46% of the popular vote. He would not have made it in France.

“I won’t say impossible, but I’d say it’s extremely improbable,” says Gombin of Le Pen’s chances of winning the 2017 presidential election. The outsider party doesn’t have allies to join forces with in the second round, and tactical voting by other parties has stopped it before. When Jean-Marie Le Pen got through to the second round of the presidential election in 2002, it came as a thunderbolt of shock. He was squarely beaten when 82% of voters from all parties opted for Jacques Chirac to keep him at bay. This time, there will be no shock – and it could be much closer.

‘Many voters are still afraid of the party’ ... Graffiti on the wall of a Front National campaign office in Trèbes, southern France. Photograph: Pascal Pavani/AFP/Getty Images

At Le Pen’s headquarters, the biggest challenge is winning over new voters – particularly older voters. In general, over 60s turn out to the ballot box – they did so for Trump – but in France they are also the most sceptical and least likely to vote for Le Pen, put off by warnings of chaos if she ever took power and worried about the impact her drive to quit the euro would have on their savings.

Louis Aliot is a Front National MEP from the south-west of France and one of Le Pen’s deputy leaders. He is also her romantic partner of seven years. Compared with the female partners of other presidential candidates – including the Welsh wife of the right’s François Fillon or maverick independent Emmanuel Macron’s wife, who is 24 years his senior and met him when she was his teacher – Aliot is less targeted by celebrity magazines and is allowed to get on with his job. Le Pen, twice divorced, rarely mentions her personal life, even if she once posted a selfie of herself kissing Aliot in a garden centre to counter a suggestion made in a magazine that their relationship was on the rocks.

Aliot says Trump’s psychological boost to Le Pen comes from the fact that the Trump campaign proved establishment predictions so wrong. “People have seen that when the entire media, elite and economic world say: ‘Watch out,’ when they demonise someone and manipulate the polls, all that can prove false in the end,” he says. “People think: ‘They said that person would never reach power and they did.’ So they say to themselves that someone else might, too. It changes the way people think.”

The key question is whom Le Pen would face if she made it to the final round. Polls currently show it is likely to be François Fillon, the rightwing former prime minister under Sarkozy, who is the candidate for Les Républicains. Fillon’s hard-right, socially conservative line on family values and “the Christian roots of France”, his emphasis on “patriotism”, his hard line on immigration and Islam and his pro-Putin foreign agenda overlap with some of Le Pen’s key ideas, which could prove dangerous to her.

But Fillon is also a self-declared fan of Margaret Thatcher, and his plan for free-market reform to radically shrink France’s ever-present state is seen as a gift to Le Pen, who runs a leftwing economic line of state protectionism, vowing to shield the vulnerable against the ravages of Fillon’s privileged class. “For us, honestly, he’s a better candidate than others,” says Aliot, warning that Fillon’s hardline positions make him “repulsive” to the left, who won’t want to mobilise a tactical vote for Fillon to keep Le Pen out.

“The need in France to score higher than 50% to win the presidential final round is something I think is still not possible for Le Pen, but that doesn’t mean she doesn’t have reason to hope,” says Jean-Yves Camus, director of the Observatory of Radical Politics at the Jean Jaurès Foundation in Paris. “Women voters are particularly important for Le Pen.”

Le Pen has managed to attract more women than in the male-dominated days of her father, but she needs to go further. “The category of women that vote most for the Front National are shop employees, including checkout cashiers,” Camus says. “They might be in precarious situations, on flexible hours, short-term contracts, earning miserable salaries, with a lower level of education and heading one-parent families – just the type of people hit hardest by the economic crisis.”

Marion Maréchal-Le Pen, centre, the more conservative niece of Le Pen, is popular within the party for promoting a more hardline social conservatism than her aunt. Photograph: Bertrand Langlois/AFP/Getty Images

One of Le Pen’s main campaign messages is to claim that Islam is a danger to women’s rights in France, and that the very presence of Islam is limiting all women’s freedoms. She has adopted a deliberately relaxed attitude to abortion in order to appeal to new women voters. But the abortion issue has led to a damaging row within the Le Pen family, revealing a party rift. Marion Maréchal-Le Pen, Le Pen’s more Catholic, more rightwing and more socially conservative niece, is pro-life and unafraid to say so. At 27, she is France’s youngest MP, extremely popular among the party faithful and ambitious for a leading role in the party. She would like the Front National to return unashamedly to the hardline, religious social conservatism of its far-right heritage. Her aunt believes that, to reach power, the party must court crucial voters from the left by appearing softer on social issues. The tension between the two women could prove a challenge for the campaign.

The Front National is not without problems. It is facing legal investigations into alleged campaign funding irregularities, which it denies, but which its opponents are likely to reference. And, as Dutch political scientist Cas Mudde has pointed out, “a populist radical-right candidate has still not won a true electoral majority in any established democracy in the postwar era”.

But Le Pen, who came third in the last presidential election with more than 6 million votes, says she likes a challenge. “She’s preparing for a difficult fight,” Aliot says. Her new motto is summed up by the blue rose brandished by Eastwood, something that doesn’t occur in nature, but is created – “the impossible that we can make possible”.