‘Dangerously plausible” is how one friend described Marine Le Pen earlier this week, having caught Andrew Marr’s TV interview with the French National Front leader last Sunday morning. She was one of many Britons who had never seen “Madame Frexit” — as the politician has dubbed herself — speak before.

And I wonder whether that plausibility was almost as disturbing to some as the BBC’s decision to air the interview on Remembrance Sunday. In France, the pejorative prefixes have been dropped: Marine Le Pen isn’t just “plausible”, she’s popular. And if current polls are accurate — at least six million voters so far — it seems increasingly likely that Jean-Marie Le Pen’s daughter will reach the final round of the presidential elections in April. Because, like Nigel Farage in Britain and Donald Trump in the United States before her, she knows how to tap into the single emotion that today governs voters’ decision-making: Fear.

No European country is more entitled to be fearful right now than France. Walking through the streets of Paris on the first anniversary of the mass shootings and suicide bombings that claimed the lives of 130 people last November was heart-breaking. There’s a capital that — in the space of two years — has gone from bold and proud to timid and introverted. Businesses are suffering, eyes are downcast and soldiers patrol the streets. “We’re not allowed to wait outside the school gates for our children any more,” one French friend tells me. “We’ve been told to drop off or pick up and leave immediately — and if any mum start chatting, they’re quickly dispersed.”

This is the same friend who took her four-year-old to church on Assumption Day — weeks after Father Jacques Hamel had his throat cut at the altar in Rouen by extremists — and sat through the service as heavily armed soldiers patrolled up and down the nave, going right up to the chancel beneath the pulpit from where the priest was preaching. When her son asked, “Why are they here?”, she replied: “To keep us safe.” Three months on, the French don’t feel any safer. And here is this unflappable, secularist politician and mother-of-three — the far-right with a human face — promising to protect the country against devastating terror attacks, rapid de-industrialisation and the refugee crisis.

“Every country has the right to defend its own interests,” she told Marr — who looked a little unnerved himself by Le Pen’s credibility, expecting, as everyone else probably did, some kind of rabid, vitriol-spewing monster, and not a stern-faced blonde, a little too heavy on the eyeliner. “Not all those who are opposed to mass immigration are racist. It’s not racist to say that we cannot take care of all the poverty in the world, or take care of hundreds of thousands of people arriving here, because our first obligation is to protect the French people.”

Cutting ties with her National Front founder father — whom she expelled from the party in 2015, after he called the Holocaust “a detail of history” — was where it all started going right for Marine Le Pen. Never mind that many of her followers are unashamed fascists (the number of swastikas I saw graffitied on walls in the south of France, her stronghold, over the summer, was sickening). Never mind that, as the French equivalent of a hatched-faced, Range-Rover-driving Sloane who grew up in bourgeois Neuilly-sur-Seine, but has adopted a mockney accent and professes to work “in the name of the people”, she’s a social fraud.

This former lawyer is serious, unflinching and has more brain cells than Farage and Trump combined. And her campaign to de-demonise the National Front is working. She’s hostile to Brussels, against free trade and against Nato (“What is Nato protecting us against?” she sneered on Marr’s show. “A military attack from Russia? Just saying that brings a smile to my face”), and she would, without doubt, break up the European Union within days of becoming president. “Yet people will now openly admit at dinner parties that they’re going to vote for her,” I’m told. “Which is a big shift. She’s no longer something you lie or even whisper about. And that’s increasingly been the case since the November 13 attacks.”

Sarkozy may be doing his best to mimic Le Pen — and he gets as near as he dares to her rhetoric — but with his candidacy still hanging in the balance, and Hollande’s Socialist Party in its self-imploded state, there isn’t much to hold her back. Certainly not the anti-woman sentiment that, in part, killed Hillary Clinton’s presidential ambitions; that doesn’t exist in France. When it comes to the vote, people may simply forget that Le Pen has likened Muslims praying in the street to “an occupation”, and was once taken to court on charges of “inciting hatred”, and decide instead that Jean-Marie Le Pen Lite is the only way to go — as his daughter puts it — in “the building of a new world”. That members of France’s powerful anti-fascist Left-wing would clash violently with that new world, almost certainly leading to rioting in the streets, may not be a consideration.

Defending his decision to interview Le Pen to those who saw it both as a kind of British media baptism and an affront to France’s fallen soldiers, Marr asked whether it was possible to ignore a woman who “could, under some circumstances, become the next French president?” The question was chilling. Because you ask yourself what those circumstances could be — and the answer is: These.

— The Telegraph Group Limited, London, 2016

Celia Walden is a British journalist, novelist and critic.