Even in France, however, the political extremes rarely shake hands in public.

The comprehensive triumph of Segolene Royal in the Socialist presidential "primary" is not the only straw in the wind of a perplexing French electoral season. Mouths gaped in France last week when Jean-Marie Le Pen, veteran xenophobe, and leader of the powerful French far right, chatted amiably in public with Dieudonne M'bala, a black comedian, one-time antiracist campaigner, now the champion of a conspiracy-obsessed and anti-semitic segment of the far left.

Dieudonne (always known by his stage name) turned up at the annual Red-White-Blue festival of Le Pen's National Front at Le Bourget, allegedly on a whim and "just to have a look". It later emerged that the visit, and the "chance" meeting between the two men was planned by senior NF officials, with Le Pen's and Dieudonne's knowledge, though the two men managed to avoid being photographed together.

What was going on? Dieudonne, 40, who has his own political comedy theatre in eastern Paris, has broken with many former friends on the left in recent years by insisting that all the ills of the world, and especially the problems of black people, can be traced to Israeli and Jewish influence. He was convicted earlier this year of making antisemitic statements.

Le Pen, 78, was once a scarcely disguised anti-semite and racist himself. Even last summer he was complaining that there were too many black faces in the France football squad at the World Cup. He has tried to re-invent himself in recent months as a democratic nationalist and patriot, open to French people of all races and religions.

Being seen with Dieudonne could help Le Pen to enlarge his appeal in next spring's presidential election.

The NF leader is convinced that he can repeat his stunning exploit of 2003 when he reached the two-candidate second round. "Look, " the handshake with Dieudonne seemed to say. "Le Pen is no racist." What Dieudonne hopes to gain from a rapprochement with Le Pen is less clear.

In the last couple of days, Dieudonne has said that the NF leader is "not the monster" that people claim and that he has "every chance" of becoming the man who brings "political revolution" to France.

The unlikely connection points to the growing chasm which now exists in French politics . . . a gulf not between left and right, but between the discredited, centrist mainstream and a jumble of paranoid, populist and often anti-democratic extremes. The extremes may hate each other, but they also recognise a common enemy.

Royal's runaway success has been based on her shrewd ability to grasp this problem and turn it to her advantage. A classic political insider, she has presented herself as a kind of centrist outsider . . . someone who understands and cares about the real problems of ordinary French people but does not offer scary or outlandish solutions (in so far as she offers any solutions at all).

Her main rival for the top prize, the almost certain main candidate of the centre-right, the interior minister, Nicolas Sarkozy, also presents himself as a plain-spoken man of the people. He insists, however, that France is ready for an abrupt shift away from the consensus left-right policies of muddle and drift of the last 23 years.

Both Royal and Sarkozy have created a kind of fervour unseen in the centre ground of French politics for two decades. It remains to be seen if that fervour will last. Many on the traditional Left of the Socialist party, or in the managerial socialdemocratic centre, still regard Ms Royal as an upstart.

President Jacques Chirac similarly hates the idea of being succeeded by a former acolyte who is openly running against the empty record of 11 years of Chiraquism.

Chirac, 74 this month, seems determined to destroy Sarkozy's chances of reaching the Elysee palace . . . to the point of reviving the unlikely threat that the old, unpopular president might run himself and split the centre-right vote.

The extremes of left and right lie eagerly in wait for this inevitable outbreak of in-fighting in the centre, which will enable them to say that mainstream politicians still care only about their personal quarrels and careers.

In-fighting is not limited to the democratic centre, however. Le Pen's National Front is also riven by internal quarrels. Unreconstructed racists within the party jeered and insulted Dieudonne when he turned up at the NF festival, forcing him to leave early.

Le Pen's own daughter, Marine, main architect of his recent lurch towards the middle, was also furious when she saw Dieudonne at the Le Bourget meeting. She had invited a militant Jewish protection group to come along to prove that the "nouveau" NF was not anti-semitic.