The Elysee Palace refused to comment today on rumours swirling in Paris that the marriage of President Nicolas Sarkozy and Carla Bruni is on the rocks, with both of them having affairs.

The French media, usually reticent about prying into the private lives of public figures, have been reporting that Bruni is having an affair with the musician Benjamin Biolay  and that her husband has turned for comfort to his ecology minister, Chantal Jouanno.

The rumour first appeared on Twitter and then on the website of the French Sunday paper, Le Journal du Dimanche, which claimed dramatically that the presidential marriage was "breathing its last breaths".

The Journal's online report said: "It's the gossip of the moment that could become the story of the year. A romance is said to have started a few weeks ago between the First Lady of France and music award winner Benjamin Biolay [he won album of the year for La Superbe at the recent Victoires de la Musique awards]."

The rumour has been picked up by at least one TV station and several online news services, one of which claims she has already moved into Biolay's Paris apartment.

Carla was the talk of Paris last week when she turned out for a state dinner for the Russian president Dmitry Medvedev wearing a figure-hugging Roland Mouret dress. The First Post reported at the time that the outfit might not have been chosen for her husband's benefit - but we had no idea a scandal of this magnitude was brewing.

Sarkozy married Bruni in February 2008 after a whirlwind romance following a blind date at a friend's dinner party. Last year, Bruni made it clear that she hoped to have children with the president. The fact that that has not happened, and her now notorious remark that she is "easily bored by monogamy", are frequently raised in Parisian gossip columns.

If Bruni has fallen for 37-year-old Biolay, it won't be her first love affair with a musician. Both Mick Jagger and Eric Clapton are among her former lovers.

As for Sarkozy, if the affair with Chantal Jouanno is real, no one is really sure whether she will be the first minister he's fallen for. His relationship with Rachida Dati - who he later sacked as justice minister - was the source of constant speculation, not least that he was the father of her daughter.