With his press conference this week - in which he declared “With Carla, it is serious” - Nicolas Sarkozy emerged as the undisputed winner of the Silvio Berlusconi Award for Europe's most embarrassing politician.

The French President's popularity ratings are plummeting just as (and because) his love life is taking off. This has nothing to do with French attitudes to sex. French voters expect their leaders to have complicated love lives. Presidential affairs are an unwritten part of the constitution, an accepted perk of office. Sarko's blooming unpopularity has nothing to do with his two divorces, or Carla Bruni's record of liaisons amoureuses with slightly knackered British pop stars.

No, Sarko's fault in French minds - which has seen his popularity rating drop a stunning seven points in a single month - is for crimes against French style, for a failure to follow the dictates of presidential savoir vivre. It is perfectly acceptable for the French president to fall in love; but for the president to fall in love in such an unsubtle and frankly American way is most definitely not.

It is Sarkozy's misfortune to appear, always, just two beats shy of being genuinely cool. He is at least two inches too short to wear mirrored aviator sunglasses; he is just ten pounds too podgy to do a Putin and take his shirt off in public; at 52, he is just five years too old to be photographed with his hand on the exposed midriff of his 39-year-old lover. These are small things, but in French eyes they matter greatly.

“Carla is living an authentic love story,” said Ms Bruni's mother. Sarkozy himself once remarked to the former Prime Minister, Dominique de Villepin: “You have to tell the French a story.” The problem with his own histoire d'amour is that it is seen in France as rather naff, more Mills & Boon than Flaubert.

Instead of wooing the former model by moonlight in the Tuileries, Sarko takes her to Disneyland Paris. Where another Frenchman's romantic gesture might involve, say, an exquisitely tasteful love poem, the president's gift is a large heart-shaped, rose-coloured diamond engagement ring designed by Victoire de Castellane at Dior - the sort of bauble Victoria Beckham might covet. In return, she gave him a Patek Philippe wristwatch, to add to the Breguet, the Rolex and the other designer watches he owns, and insists on wearing outside his shirt cuffs.

It is no accident that the nickname attached to the French president is an Americanism: “Le Président Bling-Bling”. His is a world of paparazzi and microphones, private jets laid on by friendly billionaires, and public glitz. François Mitterrand's great love was revealed when his illegitimate daughter appeared, with exquisite dramatic timing, at his funeral; Sarko and Bruni, by contrast, have already been hailed by Hello! magazine as one the “hot couples” of 2008.

“The French people did not elect him to be rock star,” declared a recent editorial in the newspaper L'Est Républicain. Sarko's problem is more that he tries to act like a rock star, and fails - which, come to think of it, is also true of every French rock star.

From this side of the Channel, the new President's gaucheries, his nouveau riche excesses and occasional faux pas are merely comic, even refreshing after the stiff pomposity of the Chirac years. Yet for many Frenchmen and women, and not merely older traditionalists, the soap operatic “Sarko Show” is mortifying, yet another example of Anglo-American celebrity culture eating away at French standards.

Sarkozy came to power six months ago, promising a “rupture” with the old ways. Informal, energetic, self-confident and direct, his style offered an extraordinary contrast to the aloof, decorous, almost monarchical presidency forged by Charles de Gaulle. Try to imagine the whiskery old general in jogging shorts, and you get an idea of the scale of cultural change that Sarko embodies.

If there was one quality the old presidency exuded, and Sarkozy openly defies, it is discretion, most notably in affairs of the heart. Giscard d'Estaing, Mitterrand and Chirac were all notorious, and secretly admired, for their numerous affairs. Indeed, as Christophe Dubois and Christophe Deloire write in Sexus Politicus, their bestselling book on French presidential bed-hopping: “Far from being a flaw, to cast yourself in the role of seducer is without doubt an important quality in our political life.”

Sarkozy claims that by bringing his own love life into the open, he is “breaking the hateful tradition of hypocrisy”, but in reality, down the years, all the presidents' women have been common knowledge, without being advertised. I used to live in the same Paris street as Chirac's mistress: riot police would close off the road for a couple of hours whenever he visited her. The local shopkeepers would simply nod appreciatively: “Ah, the Monsieur le Président is here for le cinq à sept.”

Where Sarkozy has broken the rules is by parading his love affair for the cameras at a time when most French people are deeply unhappy. The French economy remains in a parlous state, and while the President goes on exotic foreign holidays with a 26-car motorcade and a beautiful Italian-born heiress, French people are feeling poorer than at any time since the early 1990s.

The French President's mistake is to fall in love in a way that is distinctly un-French, and insufficiently presidential. As his love affair with the French public turns increasingly sour, Sarko needs to change the plot of this story and stop wearing his heart, like his designer watch, on his sleeve.

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