Under a sea of fluttering pink and blue flags, the Manif Pour Tous (Demo for all) movement's complaints were eclectic and apocalyptic – with a dash of paranoia and conspiracy thrown in for good measure.

"If we don't stop this government there be no future for France," said Médéric, 20, a student. "The family is at risk. France is at risk. You wait, it'll be euthanasia next."

On Sunday, protesters – 80,000 police said, 500,000 claimed the organisers – again took to the boulevards of Paris and Lyon in a show of force against the French government and in support of "the family". In case anyone was in doubt about what those words meant, the logo on the flags, badges, stickers and banners showed a "traditional" family: father, mother, son, daughter.

The protesters were united against gay marriage and adoption first. They lost that battle last April when parliament approved same-sex marriage. Since then, they have continued their opposition but moved on to "the family", which they believe is threatened by a proposed family law expected in the spring.

Recent demonstrations, however, are a vocal and visible expression of a more febrile atmosphere spreading across France, where the popularity of the Socialist president, François Hollande, is at rock bottom, the mainstream centre-right opposition has no clear leadership, and the far-right Front National is forecast to make significant gains in local and European elections.

The widespread sense of dissatisfaction and disillusion has encouraged extremism, as seen at a Paris "Day of Anger" protest last Sunday, which degenerated into antisemitic slogans, including "Jews out", Nazi salutes and quenelles, the trademark of controversial comedian Dieudonné M'bala M'bala.

Hollande describes the movements as "repressive and regressive", while the interior minister, Manuel Valls, has likened the atmosphere to the economic, social and political crisis that brought violent "anti-politics" demonstrations to France in the 1930s.

If Sunday's demonstrators spoke of despising the government, Valls made it clear the feeling was mutual. He told Le Journal du Dimanche that the country was witnessing the formation of a "Tea Party à la Française". Recent protests were, Valls declared, a "revolt of the antis: anti-elite, anti-state, anti-tax, anti-parliament, anti-journalists … but also and above all, antisemites, racists and homophobes. Put simply, they are anti-republicans," he said.

Symbolic of the sense of collective hysteria was the row last week over so-called gender theory, which protesters claimed was being taught at schools. Individuals with right-wing links were accused of spreading unfounded rumours that the government's ABCD of Equality programme, aimed at ending sexual stereotyping in schools, involved "masturbation classes". As a result, parents at 100 schools pulled their children from classes, convinced the government was meddling with their identity and sexual orientation.

A cartoon in Le Parisien lampooned the scaremongering, showing a boy asking his father to tell him a scary bedtime story. The father replies: "The government plans to make mothers have abortions and put the foetus in the womb of another woman who will sell it to a homosexual couple who will decide whether to bring it up a girl or a boy."

Laurent Gougeon, a printer who attended the Paris protest with his wife and son, said he was against IVF for same-sex couples and the teaching of gender theory, and was unconvinced by official denials that any such thing was happening.

"There is a threat to the family in France today. If we don't do something the family will cease to exist," he said.

A retired couple, who did not want to be named, had driven from Normandy to attend the protest. "Look around you, here are traditional French people who don't normally demonstrate. We are good citizens. We go to work and we mind our own business, but we are afraid for our children. The government wants to destroy the family," said the woman.

Maylis Gillier, a 19-year-old student, agreed: "The government is trying to create a new type of family, which is not natural. We are very against surrogacy and the marketing of women in this way."

Her friend Domitille Le Prince added: "We're called extremists because we don't think same-sex marriage is natural. Nobody is listening to us. They talk about equality as if it means you can do what you want and somehow everything is rosy. But it's not fine. It's not rosy."

A group of young men and women calling themselves the Salopards (Bastards) and wearing pink dungarees "to show you can be against gay marriage without being homophobic", was also there to "defend the family".

Jessica, 24, was one of many to voice the wider malaise. "This government has nothing but contempt for us. Nobody is listening. We are not traditional, old, French Catholics; we are young and we want to be heard," she said.