None of these stories have the tiniest grain of truth. All are hoaxes, inventions or malicious rumours, often far right or racist in tone or vocabulary.

For several months, such stories have been spreading through France by word of mouth, text, or email. Despite rebuttals, they constantly resurface on the chat lines of populist websites that claim to reveal the truth that the mainstream media hides. Some, such as the allegation that Ms Taubira is a multimillionaire, pop up on more respectable "question and answer" sites online. The rumours surf on the fractious, insurrectionary mood into which France has plunged in recent weeks. They also help to deepen it.

Similar nonsense circulated during Nicolas Sarkozy's presidency. But the intensity, and evident political spin, of the electronic rumour-mongering increased since the left won the presidential and parliamentary elections last year.

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"We are faced with a flood of anti-left hoaxes – so many that we don't have time to counter them all," said Guillaume Brossard, who runs Hoaxbuster, a French site which identifies and corrects internet lies. "Such stuff existed under Sarkozy, but nothing like as much."

France, like the US, is vulnerable to rumour-mongering because it has an instinctive distrust of Paris, politicians and the media. The late President François Mitterrand did, after all, hide an illegitimate daughter for most of the 14 years of his presidency. The mainstream media has, until recently, had a poor record of exposing political scandals.

Rumour is especially virulent when France is angry and depressive. A leaked report by regional prefects – national government administrators – last week described the nation's mood as "dangerous", especially in rural areas and among the provincial middle classes.

The economy is struggling. The Hollande administration is stumbling. Taxes are being increased to reduce persistent budget deficits. France, en masse, constantly demands change, but the French individually resent, and resist, all changes.

The lie-mongering which is thriving in this atmosphere – and also darkening it – is not just anti-left or anti-Hollande. It plays to a wider, hard-right agenda.

Pascal Froissart, an academic who has written a book on the role of rumour in French history, said: "The fear encapsulated in these messages is anti-institution and anti-establishment. They imply that the 'elites' are a unified bloc opposed to the 'real' people of France."

Most of the stories are self-evident nonsense, but that does not stop them from spreading. The allegation that Ms Taubira earned €58m last year is attributed to an American magazine called People With Money. The magazine does not exist. Both it – and the Taubira story, complete with faked front page – are figments of the imagination of a would-be satirical spoof website. They have been traded from blog to blog and email to email as if they were real.

The evidence that Ms Taubira's son is in prison for murder is a fake newspaper cutting, which has been circulating online since April. This purports to be a tear-jerking letter to the justice minister from the distraught mother of her son's "victim".

The letter is "signed" by a real person from Besançon in eastern France. She told her local newspaper that she has not lost a son, did not write the letter and has "nothing against" Ms Taubira.

The origin of the tentacular rumours that mayors of provincial towns have been paid to import black people from the Paris suburbs is harder to identify. Geneviève Gaillard, the Socialist mayor of Niort in central France, began a lawsuit for defamation against "persons unknown" last month. The local rumours had expanded to an equally baseless story that Ms Gaillard had secretly married a black man.

Similar stories have spread, partly by word of mouth, partly by email, text and blog, in Poitiers and Limoges. Local officials say that the rumours bear the linguistic imprint of the far-right National Front, which hopes to make record gains in municipal elections in March. It denies all responsibility.