Europe, says Bernard-Henri Lévy, will collapse if Brexit goes ahead. “It will collapse because when the body is deprived of its brain and its heart, its spirit dies. Britain is not just an additional piece of the European Union, it is the brain.” I never expected to hear a Frenchman say that, certainly not a great French intellectual. But there’s more: “Brexit will be a much bigger catastrophe than most people expect or think, a catastrophe for Britain and a catastrophe for Europe. Europe is unthinkable without Great Britain. Everyone who reflects deeply about Europe knows that the UK is its beating heart.”

Britain the brain and heart of Europe? I thought the French saw us as, at best, an American puppet or, at worst, a noisy neighbour. He has now written a play to make the point that Britain matters — more, perhaps, than anything. I’ll come back to that in a moment.

Lévy is the Frenchest of Frenchmen. He is known as BHL and generally accepted as the country’s most prominent public intellectual. He is just the sort of thing we anti-intellectual Brits tend to mistrust. For all his Anglophilia, this is an aspect of the British he does not like.

“Anti-intellectualism is a bad idea because it makes us closer to populism, to all of that, so it’s always a mistake. Intellectuals make some huge mistakes but anti-intellectualism is a mistake in itself.”

There are other things wrong with Britain: Boris Johnson comparing the EU to Napoleon and Hitler; Nigel Farage — “a joke, bullshit, crazy”. But France, too, is afflicted with second-rate politicians: “It’s crazy, there’s a lack of grandeur in French and English politics, also in Italian politics. This is part of the problem.”

He voted for Emmanuel Macron and clearly knows him well — he knows everybody who is anybody well — and probably better than he is letting on. So will the president succeed in his Thatcheresque battle against the unions?

“He is succeeding and I am sure Mrs Thatcher is one of the examples he has in mind during these few weeks.”

To inflame further the affront to British sensibility, Lévy is not just extravagantly clever but also elegantly so.

His baroque hairdo is famous, as are his suits — black, deliriously expensive, with high-waisted trousers — and his shirts, white and so perfect he must change them every hour or so. No tie, of course, and four or five shirt buttons undone to expose a dart of toned flesh.

He is lounging on a sofa in the library of a very expensive Paris hotel. He could not look more at home.

He is 70 this year. Surely he has a fitness regime? He’s not going there. He keeps fit, he says, “by dreaming, continuing to dream. Shimon Peres said the measure of your youth is the number of dreams that you have.”

There must be error in so much perfection. We expect our thinkers to be fat and unkempt, or thin, spotty, leather-jacketed Marxoids. Never mind, he’s on side when it comes to British greatness. Now his play — Last Exit before Brexit — is his attempt to make us change our minds.

“It’s a warning, a last signal, my modest contribution.” It will be performed for one night only in London.

“Play” is not quite the right word; lecture may be closer. The only character is called Bernard-Henri Lévy who is stuck in a hotel in Sarajevo — “a very symbolic place, a place at the borders of Europe”. He is trying to write a speech about Brexit for a conference about, well, Brexit.

The speech is haunted by real but imagined characters. So he dreams of a perfect cabinet — Michel Houellebecq, the notorious French novelist, would be, for some reason, minister for animal welfare. Minister of religion would be the militant atheist Christopher Hitchens who was, in a way, the one British public intellectual with the scope, chutzpah and style of Lévy.

Another ghost in the play is Jeremy Corbyn. Don’t get him started on Corbyn . . . or, rather, do.

“For a century we’ve known Corbyn by heart in France. We anticipated him, we had some leftist leaders who said anti-semitism was a normal reflex of the downtrodden.”

The BHL character muses that, for the sake of the left, Corbyn has to accept anti-semitism — “to accept that the cursed and the damned of the earth have the right to be anti-semitic”.

A lifelong supporter of Israel, he described last week’s killing of at least 60 Palestinian protesters as “heartbreaking”. No clear response would be possible, he said, “if we don’t take in consideration the strategy of Hamas, who were at the doors of the mosques calling for candidates for martyrdom, then pushing them to the front of the crowd and promising money to their families”.

A Jew himself, Lévy is appalled by the anti-semitism in the Labour Party. But he seems even more revolted by the response of the left-wing film maker Ken Loach to a question about the Holocaust: “He was disgusting when he was asked what he thought about Holocaust denial, his reply was that history has to be discussed. He was giving credit to the denier David Irving and to people who embrace Irving. It is disgusting to see a man of the talents of Ken Loach not finding anything else to reply.”

Of course, it is not just in Britain that anti-semitism is resurgent. It is on the rise in France and eastern Europe. The significance of this goes to the heart of a crisis in Lévy’s politics.

Anti-semitism is a sign that the evils of the past can rise up to subvert the values of the liberalism that emerged in Britain in the 18th century and spread across Europe and America. So, of course, is Donald Trump and so is Brexit. Here he acknowledges the folly of liberal complacency: “We thought Europe was a done job.” Can Anglo-Saxon liberalism reassert itself? Nobody — not even BHL — knows.

He was born in Algeria and soon afterwards the family moved to France. His father was a successful businessman and BHL’s fortune is more than £100m. Did this influence his thought? “It gave me some freedom of course, but no, I don’t think it influenced me further than that.”

His intellectual character, he says, was formed by French philosophers and British adventurers. He identifies with Lawrence of Arabia and Lord Byron fighting for Greek independence. Inspired by them he went to dark and dangerous places to research his book on the killing of the US journalist Daniel Pearl in 2002. And he plunged into the Bangladesh war of liberation in 1971 for another book.

He says he experienced no anti- semitism growing up because it simply was not around then. For this and other symptoms of the anti-liberal backlash he blames “populism” with the implication, in the case of Brexit, that people were too stupid to be asked to vote.

“You were asked a very simple question about a very complex problem and this was really the sin of the whole affair. Those who decided to ask for a yes or no answer to such a huge, complex issue were really irresponsible. The question of the UK in Europe is a question of spirit, of heart, of memories, of war and peace and of the very constituency of the UK. What is the UK? What is Europe? To reduce that to two lines like the language of a computer is a crime of the spirit.”

Populism in France is manifested in the electoral success of, on the far right, Marine Le Pen, and on the far left by Jean-Luc Mélenchon.

“Mélenchon-Le Pen is our Brexit. Populism was defeated by Macron but it might not be defeated for ever.”

What about the even more disturbing signs that Poland and Hungary are peeling away from liberal Europe? “True. In the play, TV screens on the wall show the breaking news that Hungary is joining the rouble zone and Putin is printing drachmas so Greece can leave the euro.

“We clearly underestimate the forces against us, against our brotherhood and our greatness. We have greatness and we have two players against this, Putin and Trump. All that happens, including Brexit, comes from those two players who are very bad. We underestimate their role in this game.”

There are big things wrong with his analysis. Most obviously the Brexit vote was not simply caused by public misunderstanding of the question. And the new anti-liberalism is not a populist scam devised by a Putin-Trump axis. It was a damning and accurate critique of the failures of postwar liberalism.

There are also more obscure matters. In his biography he forgives Jean-Paul Sartre for his craven Maoism. This is just plain wrong. Mao killed about 10 times more Chinese than Hitler did Jews.

Nevertheless there is a greatness about Lévy, a certain French glory. His liberal fervour is mesmeric and genuine; he wants you to be engaged and you have to be at your best either to agree or disagree. He is also physically courageous, an English adventurer, a political romantic.

And there’s that magnificent suit, that dazzling shirt. I ask him about a quote from Baudelaire: “Dandyism is the last flicker of heroism in decadent ages.” Does he identify with that?

“No. I love Baudelaire. But no.”

A pity. I thought it caught him exactly.