THE French were pondering an intriguing question last week as their president, Nicolas Sarkozy, battled to win back ground after a catastrophic collapse in the polls: was his fashionable Italian wife turning him into a better, more sensitive man?

According to reports, Carla Bruni-Sarkozy, the singer and former supermodel whom he married two months ago, has been trying to “sensitise” the president to art and open his eyes to the plight of immigrants.

Bruni, who was widely praised for her poise and elegance during the couple’s recent state visit to Britain, was also reported to have been teaching him manners. When he lit up a fat cigar at a dinner party one night, she quickly took out a cigarette and asked: “Is it all right if we smoke here?”

Bruni has become the key component in what was described by one commentator as a “vast communications operation” designed to show that the president, who has promised to modernise France through a programme of economic and social reforms, was also changing for the better.

It seems to be working: a poll showed approval for the “nouveau Sarko” rising by three points to 40% last week.

His former wife Cécilia claimed that he suffered from a “behavioural” problem and the public’s disenchantment was fuelled by his quick temper and penchant for “le bling” - designer sunglasses, flashy watches and the private jets of billionaire friends.

Bruni, by contrast, has been applauded for bringing a touch of class to the Elysée Palace.

Her “conquest of Britain” has been followed by reports that she is trying to rally the trendy Parisian left to her husband, hosting small dinner parties to introduce him to friends from the arts world, where he has long been regarded as an uncultured and dangerous rightwinger.

It is not known what Bruni – from a wealthy and highly cultured Italian family - thinks about Johnny Hallyday, the ageing French rocker whom Sarkozy has idolised since his youth; or Jean-Marie Bigard, the country’s most vulgar comedian - a sort of French Bernard Manning – who was included in the presidential entourage last year for an audience with the Pope.

Bruni’s civilising mission included an attempt to take her husband to the Tate Modern gallery to see an exhibition of French artists during their London stay although the visit was apparently vetoed for security reasons.

According to the magazine L’Express, Bruni also took Sarkozy to visit an African immigrant family so he could see their difficult living conditions. Sarkozy has been blasted by the left for a programme of immigrant expulsions and for being “insensitive” to the plight of the poor.

Bruni has even whispered: “Listen,” to her husband when she has noticed him fidgeting in meetings and there is evidence that she is exercising an influence beyond changing his behaviour. When it was announced that Georges-Marc Benamou, a left-leaning journalist and writer who served as Sarkozy’s cultural adviser, was being eased out in exchange for a plum posting as head of the Villa Médici, a French cultural institute in Rome, Bruni showed her husband Italian press articles arguing that the post was too important to award as a consolation prize to a crony.

The French première dame’s sister, Valeria Bruni-Tedeschi, an actress, was said to have been appalled by the idea; the job had already been offered to Olivier Poivre d’Arvor, an Italian-speaker and head of France’s institute for international cultural exchange. He had drawn up a plan for the relaunch of the Rome institute.

Benamou, meanwhile, had said he was looking forward to the job so that he could get on with his writing. The appointment has now been put on hold, pending the opinion of a presidential commission.

“Inevitably, the wife of a head of state will speak to her partner and that will influence him,” said Claude Guéant, the president’s chief of staff.

That was certainly the case with Cécilia, who had played a key role as an adviser and was quoted as saying that only she could control Sarkozy’s behaviour. Some have dated his troubles to the moment of her departure last October: she said she had always ensured that he was in bed early but that after she left he made a habit of staying up late with friends to indulge his passion for karaoke.

“Sarko”, it seems, functions much better in the presence of women, regardless of whether he is married to them. Michèle Alliot-Marie, the interior minister, noted recently that on the occasions when he had lost his temper in public none of his numerous female ministers had been present.

Another part of the Sarkozy reinvention involves letting François Fillon, the prime minister, take the heat for unpopular policies such as dispatching French troops to Afghanistan. As Sarkozy’s approval rating went up, Fillon’s was plummeting.

In other areas, however, Sarkozy is finding it harder to suppress himself. The American embassy received a call from the Elysée last week urging it to cross Cécilia and Richard Attias, her new husband, off the guest list for a dinner hosted by the ambassador on Tuesday night, according to a friend of the couple. It refused.

It is hoped that Franco-American relations will not suffer as a result.

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