Love, says France's greatest living philosopher, "is not a contract between two narcissists. It's more than that. It's a construction that compels the participants to go beyond narcissism. In order that love lasts one has to reinvent oneself."

Alain Badiou, venerable Maoist, 75-year-old soixante-huitard, vituperative excoriator of Sarkozy and Hollande and such a controversial figure in France that when he was profiled in Marianne magazine they used the headline "Badiou: is the star of philosophy a bastard?", smiles at me sweetly across the living room of his Paris flat. "Everybody says love is about finding the person who is right for me and then everything will be fine. But it's not like that. It involves work. An old man tells you this!"

In his new book, Badiou writes about his love life. "I have only once in my life given up on a love. It was my first love, and then gradually I became so aware this step had been a mistake I tried to recover that initial love, late, very late – the death of the loved one was approaching – but with a unique intensity and feeling of necessity." That abandonment and attempt at recovery marked all the philosopher's subsequent love affairs. "There have been dramas and heart-wrenching and doubts, but I have never again abandoned a love. And I feel really assured by the fact that the women I have loved I have loved for always."

But isn't such laborious commitment a pointless fuss in this age of ready pleasures and easily disposable lovers? "No! I insist on this – that solving the existential problems of love is life's great joy," he says and then looks across the coffee table at his translator, Isabelle Vodoz, with a big, half-ironic grin. "There is a kind of serenity in love which is almost a paradise," he adds, popping a biscuit in his mouth and giggling. She giggles, too. "I am not only his translator," she tells me later. Below this sixth-floor apartment, an RER train screeches along the rails out of Denfert-Rochereau station.

I think about the distinction Badiou describes in In Praise of Love. "While desire focuses on the other, always in a somewhat fetishist[ic] manner, on particular objects, like breasts, buttocks and cock," writes Badiou, "love focuses on the very being of the other, on the other as it has erupted, fully armed with its being, into my life that is consequently disrupted and re-fashioned."

In other words love is, in many respects, the opposite of sex. Love, for Badiou, is what follows a deranging chance eruption in one's life. He puts it philosophically: "The absolute contingency of the encounter takes on the appearance of destiny. The declaration of love marks the transition from chance to destiny and that's why it is so perilous and so burdened with a kind of horrifying stage fright." Love's work consists in conquering that fright. Badiou cites Mallarmé, who saw poetry as "chance defeated word by word". A loving relationship is similar. "In love, fidelity signifies this extended victory: the randomness of an encounter defeated day after day through the invention of what will endure," writes Badiou.

But this encomium to creative fidelity surely shows Badiou to be a man out of his time. "In Paris now half of couples don't stay together more than five years," he says. "I think it's sad because I don't think many of these people know the joy of love. They know sexual pleasure – but we all know what Lacan said about sexual pleasure."

Indeed. Jacques Lacan argued that sexual relationships don't exist. (Badiou will shortly publish a book of conversations between Lacan and his biographer, Elisabeth Roudinesco.) What is real is narcissistic, Lacan suggested, what binds imaginary. "To an extent, I agree with him. If you limit yourself to sexual pleasure it's narcissistic. You don't connect with the other, you take what pleasure you want from them."

But wasn't the rampant hedonism unleashed during Paris's May 1968 événements, in which Badiou participated, all about libidinal liberation from social constraint? How can he, of all people, hymn bourgeois notions such as commitment and conjugal felicity? "Well, I absolutely agree that sex needs to be freed from morality. I'm not going to speak against the freedom to experiment sexually like some old arse" – "un vieux connard" – "but when you liberate sexuality, you don't solve the problems of love. That's why I propose a new philosophy of love, wherein you can't avoid problems or working to solve them."

But, he argues, avoiding love's problems is just what we do in our risk-averse, commitment-phobic society. Badiou was struck by publicity slogans for French online dating site Méetic such as "Get perfect love without suffering" or "Be in love without falling in love". "For me these posters destroy the poetry of existence. They try to suppress the adventure of love. Their idea is you calculate who has the same tastes, the same fantasies, the same holidays, wants the same number of children. Méetic try to go back to organised marriages – not by parents but by the lovers themselves." Aren't they meeting a demand? "Sure. Everybody wants a contract that guarantees them against risk. Love isn't like that. You can't buy a lover. Sex, yes, but not a lover."

For Badiou, love is becoming a consumer product like everything else. The French anti-globalisation campaigner José Bové once wrote a book entitled Le Monde n'est pas une Marchandise (The World Isn't a Commodity). Badiou's book is, in a sense, its sequel and could have been entitled L'Amour n'est pas une Marchandise non plus (Love Isn't a Commodity Either).

Surely that makes him an old romantic? "I think that romanticism is a reaction against classicism. Romanticism exalted love against classical arranged marriages – hence l'amour fou, antisocial love. In that sense I'm neither romantic nor classic. My approach is that love is both an encounter and a construction. You have to resolve the problems in love – live together or not, to have a child or not, what one does in the evening."

This new book on love is an application of Badiou's singular philosophy of the subject and his outré conception of truth set out in incredibly forbidding books steeped in mathematics and deploying Zermelo–Fraenkel set theory, such as Theory of the Subject, Being and Event and Logics of Worlds. These books have led him to be hailed as a great philosopher. "A figure like Plato or Hegel walks here among us," Slavoj Žižek has written.

Badiou's philosophy of the subject is an extrapolation of Sartre's existentialist slogan "Existence precedes essence" and incorporates a communist hypothesis that Althusser might have liked. It's also a rebuke to postwar and often postmodern French philosophers such as Derrida, Lyotard, Baudrillard and Foucault with whom he argued and all of whom he has outlived. What is a subject for Badiou? "Simone de Beauvoir wrote that you are not born a woman, you become one. I would say you are not a subject or human being, you become one. You become a subject to the extent to which you can respond to events. For me personally, I responded to the events of '68, I accepted my romantic destiny, became interested in mathematics – all these chance events made me what I am."

How does truth come into all this? "You discover truth in your response to the event. Truth is a construction after the event. The example of love is the clearest. It starts with an encounter that's not calculable but afterwards you realise what it was. The same with science: you discover something unexpected – mountains on the moon, say – and afterwards there is mathematical work to give it sense. That is a process of truth because in that subjective experience there is a certain universal value. It is a truth procedure because it leads from subjective experience and chance to universal value."

Badiou's very odd, post-existentialist, heretically Marxist and defiantly anti-parliamentary conception of politics has a similar trajectory. "Real politics is that which gives enthusiasm," he says. "Love and politics are the two great figures of social engagement. Politics is enthusiasm with a collective; with love, two people. So love is the minimal form of communism."

He defines his "real politics" in opposition to what he calls "parliamentary cretinism". His politics starts with subjective experience, involves a truth procedure and ends, fingers crossed, in a communist society. Why? "It's necessary to invent a politics that is not identical with power. Real politics is to engage to resolve problems within a collective with enthusiasm. It's not simply to delegate problems to the professionals. Love is like politics in that it's not a professional affair. There are no professionals in love, and none in real politics."

Badiou hasn't voted since 1968, a habit he didn't break in France's recent presidential election. But he says he is writing a book about politics, a sequel to his 2007 succès de scandale De quoi Sarkozy est-il le nom? (The Meaning of Sarkozy), in which he notoriously called the last French president "rat man" for playing on public concerns about crime and immigration. Earlier this month he wrote a marvellously vituperative column for Le Monde that has been trending across the francophone world. Sarkozy and Marine Le Pen, he maintained, weren't the only politicians responsible for "the rise of rampant fascism" in France. He argued that there was a Socialist party tradition of colluding with right-wing racism – from Mitterrand through Jospin and, no doubt, into Hollande's first term. Ingeniously, Badiou suggested that mainstream politicians were disappointed in the French people for having a racist sensibility for which they, the "parliamentary cretins" (aided by some fellow intellectuals whom Badiou excoriated), were actually responsible for creating. "It is this stubborn encouragement of the state that shapes the ugly racialist opinion and reaction, and not vice versa … In order to improve democracy, then, it's necessary to change the people, as Brecht ironically proposed." The article nicely conveys his sense that democracy as currently practised in France is a charade inimical to true rule of the people.

Badiou's far-left politics were burnished in the late 60s. In 1969, he joined the Maoist Union des Communistes de France marxiste-léniniste (UCFml), enthused by Mao's Cultural Revolution that had begun three years earlier. Just as he has been faithful to all but one of his lovers, he has remained true to Maoism. Marianne magazine called him a "fossil of the 60s and 70s", but Badiou is unrepentant. He still holds that the Cultural Revolution was inspirational, as deranging and fertile for him as falling in love – despite the deaths, rapes, tortures, mass displacements and infringements of human rights with which it has been associated.

When I ask him why, Badiou explains that the success of Lenin's disciplined Bolshevik party in the 1917 October Revolution spawned a series of other workers' revolutions, notably in China in 1949. "One soon saw that this instrument that was capable of achieving victory was not very capable of knowing what to do with its victory." Maoist bureaucracy was corrupt and self-serving, party activists were bourgeois and anti-socialist, and the communist revolution under threat. "So the Cultural Revolution was important because it was the last attempt within that history to modify that in a revolutionary manner. That's to say they made an attack on the communist state itself to revolutionise communism. It was a failure but many interesting events are failures." He cites the Paris Commune and Rosa Luxemburg and Karl Liebknecht's failed German revolution among such interesting failures.

In his 2010 book The Communist Hypothesis, Badiou wrote about the importance of failure for like-minded communists (many of whom gathered with him and Žižek at Birkbeck College, London in 2009 for a conference called On the Idea of Communism). "Any failure," he writes, "is a lesson which, ultimately, can be incorporated into the positive universality of the construction of a truth." Which means that Badiou at least has not lost faith in communism. "The old Marxist idea of creating an international society is truly the order of the day now," he says. "Today things are much more international than they have ever been – commodities and people are much more international than before." So the time is more ripe than ever for international workers' revolution? "I wouldn't say that. Certainly at the world level there can be more hope than hitherto. We're climbing a very big ladder."

Badiou was born in Rabat, Morocco, in 1937. His mother was a professor of philosophy, his father a maths professor and socialist mayor of Toulouse from 1944-58. His philosophical training began in 1950s Paris. He quickly became a Sartrean, devoted to the paradoxical philosophy that, he says, involved "a complicated synthesis between a very determinist Marxist theory of history and an anti-determinist philosophy of conscience".

In a new book of essays entitled The Adventure of French Philosophy, Badiou argues that between the appearance of Sartre's Being and Nothingness in 1943 and the publication of Deleuze and Guattari's What Is Philosophy? in 1991, French philosophy enjoyed a golden age akin to classical Greece or Enlightenment Germany. Badiou's great fortune was to be part of that adventure. Like wine and cheese, French philosophy should, he says, be considered part of France's glory. "I tell our ambassadors you have with us philosophers the greatest export product."

He speaks fondly of his times at the Université Paris 8 Vincennes-Saint-Denis which, founded in the late 60s, fast became a bastion of countercultural thought. There he engaged in fierce intellectual debates with his fellow professors Deleuze and Lyotard, even though he considered them traitors to the communist cause. "These men were my rivals and my neighbours, people whom I admired and differed profoundly from."

But why, if he's right, did France have this postwar adventure, this dizzying explosion of intellectual life? "I think because of the political catastrophe in France – Pétain and the disaster of collaboration. That resulted in a philosophy that had a duty to respond to those disgraces, to propose a different way. What's more, there is a French model of being a philosopher which isn't enclosed in the academy as in England – a philosopher who is an intellectual interested in all the things in their age. Such were Diderot, Rousseau and above all Pascal."

He credits Sartre with revivifying that French model of what a philosopher could be. "All my eminent colleagues were profs because they had to live, but that wasn't their vocation – they wanted to be politically engaged public intellectuals and often artists, like Sartre. Me, too." Badiou, like a mini-Sartre, is not just a publicly engaged philosopher, but a dramatist and novelist. Unlike Sartre, he has appeared in a Jean-Luc Godard film - as a philosopher lecturer on a luxury cruise ship in 2010's Film Socialisme. His says his overwhelming ambition has been to change the relationship between workers and intellectuals. "For me what was especially important from May 1968 to 1980 was that we created new political forms of organisations linking intellectuals and workers. Those links helped me reinvent myself as a human subject. One could say that attempt failed, but I keep dazzling memories of that time." Badiou's eyes gleam as if he's recalling an old love affair he can never forget, still less disown. Perhaps politics and love are not, if you're a French Maoist, so very different.

Badiou chuckles bitterly. "France always exists through its exceptions. There are temporary exceptions that aren't representative of an overwhelmingly reactionary country but are what make it less disgusting than it would be without them. I mean exceptions like 1789, 1848, 1871, the resistance, French philosophy after the war. They are the underside to the reactionary tradition of Louis Philippe, Napoleon III, Pétain, Sarkozy." And you're one of those exceptions? "Why not? Certainly philosophy from Sartre to Deleuze and me has made France better than it would otherwise have been."