Hundreds of thousands of pro-family and anti-government demonstrators marched through Paris yesterday amid claims from a minister that France faced a return of the “sombre” and “disturbing” political divisions of the 1930s.

The stark warning by the interior minister, Manuel Valls, jarred with the prosperous, well-behaved ranks of most of yesterday’s marchers, including thousands of elderly people and families with children in push-chairs.

However, two groups of hard-right thugs were arrested as they attempted to join the protest. Scuffles broke out on the Avenue Raspail last night between riot police and about 200 hard-right youths giving Hitler salutes. They threw beer bottles at the police, who responded with tear gas.

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Yesterday’s warning by Mr Valls of “sombre forces” at work in France followed a similar but smaller demonstration last week which dissolved into running battles with riot police. Several large sections of protesters on that march carried anti-Semitic banners and chanted “Jews out of France”.

There was no sign of such banners at yesterday’s demonstration – nominally the 15th protest against the law passed last summer which made gay marriage legal in France. Yesterday’s march, which attracted about 200,000 people (the organisers claimed 500,000 attended), turned instead into a much wider protest against the alleged “familyphobe” policies of the left-wing government of President François Hollande.

Many marchers said they were protesting against the “conspiracy” of the government, and the “gay” and “feminist” lobbies, to brainwash primary school pupils into forgetting that they were boys and girls. In recent months an apparently baseless conviction that something called “gender theory” is to be imposed in France has been created by a de facto alliance of fundamentalist Catholics and ultra-right wing, anti-Semitic and anti-gay nationalists.

One banner on yesterday’s march read, bizarrely: “Gender. Never, never, never.” Another read: “The school should instruct. Only the family should educate.”

Mr Valls said in a newspaper interview yesterday: “We are witnessing a union of extremes, never before seen in France… [Last week] was the first time for a long time that people have screamed their hatred of Jews in the street.

“A block of protest is forming, a rebellion which is anti-elite, anti-state, anti-tax, anti-parliament, anti-press … but also, and above all, anti-Semitic, racist and homophobe.”

Mr Valls is playing with fire. Most of the people on yesterday’s march – and many of the protesters at last week’s “day of anger” – were radical Catholics or conservatives: anti-gay, perhaps, but not anti-Semite or anti-Republican.

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One protester, Alain, 67, a businessman, said: “Valls thinks that he can contain these protests by painting us all as dangerous extremists. When I was young, every left-winger was accused of being a communist. Now, to this government and the mainstream media, every right-winger is a fascist.”

And yet Mr Valls also has a point. France’s economic sufferings are fusing with contempt for President Hollande to dissolve barriers between radical, but respectable, conservatism and violent, new extremes (even more extreme than the National Front). This, in itself, is reminiscent of the poisonous politics of France in the 1930s.

Centre-right and even far-right politicians, such as the National Front’s Marine Le Pen, are torn between condemning and trying to channel the new radicalism. One name connects a number of recent events or phenomena, including the rise of the anti-Semitic comedian Dieudonné M’bala M’Bala and the anti-Jewish banners and chanting on last week’s march. It also arises in connection with a recent obscene internet and text campaign which persuaded hundreds of French parents that the government wanted primary school children to masturbate in class.

The common factor is Alain Soral, a 55-year-old Franco-Swiss ex-communist who preaches a new and virulent form of French nationalism. His declared aim is to unite poor people – white, brown and black – in a revolt against the “dictatorship” of capitalists, progressives, Jews and gays. Mr Soral, an avowed anti-Semite and “national socialist”, is Dieudonné’s political guru. He was long regarded as a marginal figure. No more.

Mr Valls accused him yesterday of creating a new “abscess of rampant hatred” in France. “Alain Soral, through his use of the net, the networks he has created, is uniting and federating an unprecedented front of extremes,” Mr Valls said.

Mr Soral had no connection with yesterday’s march. It was mischievous of Mr Valls to imply that he did. But many of yesterday’s marchers nevertheless swallow wholesale the distortions pedalled by Mr Soral and by Catholic extremists in recent months on “la théorie du genre” – or gender theory. They demanded the withdrawal of a pilot programme in four areas of France which seeks to steer primary school boys and girls away from gender stereotypes.

This apparently modest programme consists of trying to persuade girls that they can perfectly well drive tractors and boys that they can be ballet dancers if they want to. Harmless? Not as far as the marchers were concerned.

Adèle, 42, demonstrating with her three small children yesterday, said: “What they are really trying to do is to destroy the family. It is all part of the same plan as the gay marriage law, to impose a completely new set of values on French society.”

It was this programme which was the subject of the obscene rumour spread by text and online a few days ago by Mr Soral’s lieutenant, Farida Belghoul. Texts, tweets and emails persuaded hundreds of mostly black and Muslim parents that there would be masturbation and cross-dressing in primary schools.

More moderate protesters against gender theory have been slow to repudiate the nonsense disseminated by Mr Soral and his friends.

Béatrice Bourges is the spokeswoman for Printemps Français (“French Spring”) one of the more radical groups behind yesterday’s march – and last week’s. She is currently on hunger strike demanding the impeachment of Mr Hollande by the national assembly.

She accuses the President of “bringing France to its knees” morally as well as economically – not because of his alleged affair with an actress but by “perverting the school system” to “destroy our families”.

One of France’s most popular conservative columnists, Ivan Rioufol, of Le Figaro, accused Ms Bourges and other radical Catholics this week of “undermining their own credibility” and “playing into the hands” of the government by failing to erect firewalls between their movement and racist, “plot-obsessed” extremists.

Ms Bourges told The Independent that she tried to stop the anti-Semitic outbreaks last week. She said she had “never met this man Soral”. But she refused to repudiate the campaign which persuaded hundreds of parents to take their children out of school.

“It performed a useful function in drawing attention to the dangers of gender theory and what the government is trying to do to the family in this country,” she said.