I have been living full-time in Paris for the past four years and reporting from the city for nearly 20. I have, therefore, become accustomed to frequent street protests. But I have never seen anything quite like the anger that has been building up during demonstrations over the past few months against the government of Nicolas Sarkozy. The most recent of these was a protest I attended in Montparnasse on 14 May, which was led by hospital staff angry at proposed health service reforms.

The reforms are based on the so-called “Loi Bachelot” (Bachelot law), named after Roselyne Bachelot-Narquin, the politician in Sarkozy’s government who devised the health reforms and is trying to push them through the National Assembly. It rests on the principle that managers will decide the level of medical care appropriate to a particular hospital. This proposal, long familiar as a fact of life to readers in the UK, has provoked a furious reaction from all sections of French society.

Yet, on the surface, all seems well when I arrive at the demonstration: as I park my bike, a line of black and Arab nurses dances a salsa past the Métro Duroc. They are accompanied by rappers, trade unionists, an anarchist jazz band and stern, bossy matrons and white-coated psychiatrists from La Pitié – the hospital where the young Sigmund Freud attended Charcot’s lectures in psychiatry. It is a surreal snapshot of 21^st-century life on the Left Bank, and all suitably festive on a warm spring morning.

But you don’t have to scratch too hard to find real rage lurking beneath the surface – a rage that motivates most of these demonstrators. “We are sick of being told we have no control over our own lives,” Rachida Ahloulay, one of the dancing nurses, tells me. “It’s not just that the government is giving managers the power over medical staff,” she says, “but it means that we are degraded as citizens. And that is why France is on the edge of a serious rebellion. Anger is everywhere!”

This kind of rhetoric is being echoed all over France: in the universities, which are now permanently blockaded by staff and students; in the railway unions; among postal workers; and even in the prison service (warders recently began a series of strikes, which had never happened in France before). Little wonder that the mainstream journal Le Nouvel Observateur recently devoted an entire issue to what it called “The French Insurrection”, or that there is now serious talk in most sections of the media of a “New May ’68” – a reprise of the strikes and riots that brought France to its knees and almost felled the government of Charles de Gaulle more than 40 years ago.

The unlikely figurehead of this new popular revolt is Olivier Besancenot, a 35-year-old postman from the outskirts of Paris. Besancenot’s boyish good looks, fashionable clothes and fluently easy manner on television have made him the nation’s favourite revolutionary. Until February of this year, he was a leading figure in the Ligue Communiste Révolutionnaire (the LCR, or Revolutionary Communist League). In what is now looking like a very smart piece of PR, the LCR was then dissolved, re-emerging as the Nouveau Parti Anticapitaliste (NPA, or New Anti-Capitalist Party), a much broader coalition, formed with the aim of contesting the European parliamentary elections in early June.

Besancenot, who is now official spokesman for the NPA (there is no leader), commands a 60 per cent approval rating from French voters right across the political spectrum.

During the demonstration against the Loi Bachelot, I caught up with Omar Slaouti, a 42-year-old university professor of chemistry and long-standing colleague of Besancenot’s who is also the NPA’s candidate for the European elections for the Île de France region. Slaouti is slightly built, but has the streetwise slouch of the tough kid who grew up in the French suburbs. He also talks with a non-Parisian accent, which marks out his origins in the banlieue. I am told he is a big hit with the NPA girls.

I ask Slaouti whether a new May ’68 is really on the cards, or is it just hype? “In France now,” he says, “everything is worse than May ’68 in lots of ways – more unemployment, racial violence, real poverty, and so on. The French middle classes are poor, too – maybe the poorest in Europe. And that’s when things might change.”

This is the line that the NPA has been peddling ceaselessly, especially on television. It accounts for the party’s popularity with voters who would never normally associate with the extreme left. I spoke about this with Dr Bernard Granger, a professor of psychiatric medicine who is also the president of SCCAHP, the union of clinical heads and hospital assistants. This is a large, but historically moderate, grouping that has now sworn to bring the government down if the Loi Bachelot is passed.

“France is at a real crisis point,” Granger told me. “And the real issue is about control – who controls the daily lives of ordinary people. There is no issue more fundamental than health. Everybody knows if this law is passed, ordinary people will die.” This is the kind of grass-roots appeal that has kept the NPA’s bandwagon rolling across France.

It is likely that the NPA’s impact on the European elections will be statistically insignificant – the party is unlikely to garner more than 4.5 per cent of the vote; but as a cultural phenomenon its impact has been enormous. The NPA describes itself as being “from the street”: its celebrity supporters include the rapper Joey Starr and the footballer Franck Ribéry (as well as the decidedly un-street Ken Loach). That accounts for why the NPA is the favoured political choice of more than 40 per cent of young people in France, the vast majority of them having shown no previous interest in Trotsky, but who now proudly declare their membership of Génération Olivier.

This has created problems for the parties of the left. The Parti Socialiste (PS), the biggest party on the left, is losing young voters to the NPA in large numbers, and fast. The next most important grouping on the left from an electoral point of view, the Parti Communiste Français (PCF), has tried to make headway in a coalition with the Greens [the Left Party in fact, dissidents from the SP] called the Front de Gauche. Most young people are cynical about and bored by both parties.

“Who cares?” said Jocelyne, a Senegalese girl from the suburb of Montreuil. “It’s the same old faces – Ségolène [Royal] and her pals. They don’t care about us. They don’t know us.”

A few hours after the demonstration in Montparnasse, I watched a group of youngsters, most of them claiming allegiance to the NPA, barge their way into the entrance to the faculty building of Sciences Po on the rue de Saint-Simon, just off the Boulevard Saint-Germain. Sciences Po is a grande école, a well-funded elite institution that has mainly stood apart from the strike action which has paralysed the rest of the higher education sector. “You rich bastards!” shout the students, under the banner of a red flag with the logo of the NPA. “Why don’t you fucking come out and join the revolution?”

The Sciences Po students, most of them in neat, preppy clothes, giggle nervously, and soon retreat behind a line of heavily armed police. Yet even here, in what has historically been a rather conservative institution, a faction of the NPA is exerting a growing influence, spreading pro paganda, daubing the walls with situationist slogans and regularly disrupting classes.

I asked one of the militants at Sciences Po, “Frédéric” (he didn’t want to give me his real name), why he supports the NPA. “The NPA understand this generation better than anyone else,” he said. “They know that our degrees are worthless, that we have all been ripped off by capitalism, that we will never have proper jobs, that there is no future. They promise a different way, a real alternative.” What did that mean? “The NPA is a cultural revolution,” he said. “They are not afraid to challenge the basic principles of our society. That’s why they are exciting – they promise something real that we can make happen.”

Omar Slaouti echoed this. “What I find positive is that all of the energies, all of the anger in French society, are now flowing in the right direction, towards real change.” He said this to me as we walked down the Boulevard de Montparnasse, in the slipstream of the Bachelot demonstration. But was Slaouti seriously talking about revolution? “But of course. We are not scared of the word ‘revolution’ – that’s why young people love us. We are not afraid to say it. It’s the same in Greece, in Guadeloupe – everyone of the young generation can see that capitalism has failed and they are young enough to believe in an alternative.”

One thing is clear: the NPA may not change the world, but it is already changing French society. Government insiders now say that Nicolas Sarkozy has for the first time started to take an interest in history and, in particular, the history of the French Revolution. Given the incendiary climate on the streets of France, he might also do well to keep a weather eye on his own political future.