LONDON — In France, it is fashionable to sneer at President Sarkozy, who is supposedly too authoritarian yet not presidential enough. Private life has eclipsed public policy, say his detractors, forgetting that when he came to office last year they warned that these same policies might provoke a revolt, or even a revolution.

In Britain, where Mr. Sarkozy is on his first state visit, they can’t get enough of him — and especially of her. As the Sarkozy show hit town, Carla Bruni inevitably stole it. Greeting them at the airport, Prince Charles couldn’t help flirting with Sarko’s drop-dead gorgeous chanteuse of a wife, while she demurely batted her eyelashes. Poor Camilla managed to maintain her composure, but her feathery hat looked as if her husband might just have shot it.

Madame Sarkozy is a cross between Jacqueline Kennedy and Morticia Addams. Unashamed of her preference for haute couture rather than high culture, Ms. Bruni also subscribes to a decidedly immodest philosophy: if you’ve got it, flaunt it. (Yesterday yet another of her nude photos, admittedly 15 years old, emerged.)

The former supermodel may have the highest respect for men, but she has in the past certainly got through them faster than her new husband can befriend yacht-owning tycoons. Her latest folk album already features a sticker that boasts about how the couple stayed as guests of the Queen at Windsor Castle. The British tabloid press for once finds a foreign First Lady far more interesting than its own royal family.

This is a strangely frenetic state visit, which had to be crammed into 36 hours to accommodate President Sarkozy’s tight schedule. By comparison, President Bush’s state visit to Britain in 2003 lasted three days and the Queen’s return visit to America last year lasted five. Oddly, however, the discourtesy is not resented because the British really do want to see the cut of Sarko’s jib — and croon over Carla. Mr. Sarkozy told a rare joint session of the two Houses of Parliament yesterday that he wanted to move on from the celebrated Entente Cordiale, the Anglo-French accord signed more than a century ago, to an “Entente Amicale.” In other words, not mere cordiality but real friendship — even “fraternité” — should replace a frequently stormy relationship that boasts history’s longest conflict, the Hundred Years’ War.

Even that conflict was dwarfed by the Franco-British struggle for world supremacy that lasted throughout the 18th and early 19th centuries, ending only with Napoleon’s defeat at Waterloo.

If Mr. Sarkozy was conscious of this heavy burden of history when he spoke of “friendly rivalry” at the banquet in Windsor Castle last night, he rose above it by proposing to send French reinforcements to Afghanistan to bolster the NATO war effort there. This was music to British ears, for the British and Americans have borne the brunt of the fighting there, while France has remained nearly as aloof as in Iraq.

Even more significantly, Mr. Sarkozy has hinted that France may return to full membership of NATO in time for the alliance’s 60th anniversary next year. (It left under De Gaulle as a gesture of anti-American defiance.) In return, he wants the British to support his plan to give the European Union its own armed forces — which many in Washington and London see as a possible rival to NATO.

Nor is defense the only issue on which brotherhood means business. Nuclear power is a big French industry, which by a supreme irony has been boosted by the global warming panic. Now the British — who derive just 20% of their electricity from nuclear power, compared to 80% in France — have woken up to the fact that they will have to buy nuclear technology from the French for a new generation of power plants, or else risk becoming dependent on Russian gas and oil.

Prime Minister Brown has kept his own counsel on these diplomatic flourishes, in lugubrious contrast to the flamboyant Frenchman. Yet all these bids for reconciliation do signify a new rapprochement compared to the bad old days of Jacques Chirac — a name Mr. Sarkozy cannot bring himself to utter.

Still, the new Anglo-French entente may yet prove a formidable factor in European diplomacy, particularly as the German Chancellor, Angela Merkel, does not trust, still less like, Mr. Sarkozy. Her mistrust is heartily reciprocated.

Britain and France can no longer afford to be enemies, for one very good reason. Messrs. Brown and Sarkozy both know that perhaps a million French citizens live in Britain, most of them in London. Roughly as many Brits have houses in France, where many retire. These ex-patriots have a stake in each other’s countries that politicians on both sides of the English Channel cannot ignore.

It may not be the Field of the Cloth of Gold — the famous meeting of Henry VIII and Francis I, where the two young kings and their entourages vied with one another in chivalry, wrestling, and conspicuous consumption. You’d be lucky to catch a Scottish Presbyterian like Mr. Brown buying Mr. Sarkozy so much as a glass of Scotch. The old skinflint always raises the tax on wine (mainly French in origin, though mainly drunk by the English) a little more than on his native whiskey.

Yet Mr. Sarkozy has proved that he deserves to be taken seriously by the Anglo-Saxon powers. It would be foolish for any British prime minister — or the next American president — to ignore the little French guy with the tall Italian doll.