We all know what 'vigorous exchange of views' means. But rarely can a summit have ended with both sides boasting that their chap managed to get some juicy insults past the other fellow. Reading the press coverage on both sides of the Channel, a cartoon-like picture emerges. One imagines Tony Blair and Jacques Chirac like two Asterix characters, purple with rage, leaning towards each other with their noses squashed together.
This is not the first Anglo-French diplomatic row, of course. Lord Palmerston, on being told by his counterpart that the English had no word equivalent to the French 'sensibilitZ', replied, 'Yes we have: humbug.' And Winston Churchill had furious arguments with Charles de Gaulle, once telling him: 'Ecoutez-moi, Monsieur le GZnZral, et markez mes mots: si vous me double-crosserez, je vous liquidaterai.'
Yet there is something curious about the Blair-Chirac estrangement. Both men have gone out of their way to bring their countries closer together; Blair as the most pro-European prime minister since Edward Heath, Chirac as the first French leader to talk seriously about rejoining the Nato command. Each is comfortable in the other's language, and they share a pragmatic - or, if you prefer, opportunistic - approach to politics. Why have these two obvious soul mates fallen out?
On one level, the scrap was about farming. Blair, like all British politicians, wants to wind down the Common Agricultural Policy, while Chirac, like all French ones, wants to keep it. Having done a great deal over the years to cosy up to Paris, Blair was rather cross to find that Chirac had gone behind his back and struck a deal to keep the subsidies flowing from British consumers to his own farmers.
In the background, though, is the perennial question of the United Kingdom's place in Europe. De Gaulle vetoed two British applications to the EEC because he believed that we would never be able to turn our faces away from what he liked to call 'le grand large': the open main. The issue has never really gone away; it keeps being reborn in new shapes. Its current incarnation is France's opposition to 'unilateral' Anglo-American action against Saddam Hussein.
And here, for all their superficial similarities, Blair's approach could hardly be more different from that of his French homologue. The Prime Minister, at heart, believes in influence. Throughout the Iraq crisis, and at considerable domestic cost, he has gone along with President Bush, calculating that unquestioning support in public will win him a hearing in private.
This, mutatis mutandis, is also his policy towards the EU. Since he came to office, he has done everything he can to placate his fellow heads of government, signing the Social Chapter, going along enthusiastically with the Amsterdam and Nice treaties, even sounding positive about the federal constitution unveiled earlier this week by ValZry Giscard d'Estaing. He has been especially solicitous of French goodwill. Cast your mind back to the early days of his leadership: the Canary Wharf summit, his address (in French) to the National Assembly, the St Malo agreement setting up joint Anglo-French military forces.
And what does he have to show for it? Five years on, Chirac treats him with the same disregard that all British prime ministers encounter when the EU sets about truly important business. When it comes to enlargement, or the budget, or - above all - farm subsidies, the deal is largely done before the Brits turn up.
The fact is that arguing from within, the strategy so cherished by British diplomats, is about as clear a failure as anything in international relations can be. Diplomatic trade-offs are made on the basis of present interest, not past gratitude. Chirac was no doubt genuinely appreciative of Blair's willingness to countenance European armed forces outside Nato; but it would never cross his mind that this should lead him to make concessions over the CAP. George W. Bush is visibly touched by Britain's support over Iraq. But does anyone imagine that he will offer Blair a veto over a unilateral US attack?
Now compare this with Chirac's approach. Under his leadership, France, perhaps more than any other state, is dictating the pace and nature of the military build-up. The Quai d'Orsay takes the view that there is no point in having a seat on the UN Security Council if you do not use it. Even now, it is by no means impossible that France will eventually agree to join a military coalition in the Gulf; but not before it has squeezed every ounce of advantage from the situation.
Many commentators explain France's opposition to US policy as mere reflexive anti-Americanism. And it is true that there is something splendidly outrageous about the French foreign minister, Dominique de Villepin, demanding 'collective, rather than unilateral' action. This, after all, from the country that sank the Rainbow Warrior in a friendly port, that pushed ahead with nuclear tests in the South Pacific despite global outrage, and that, more recently, invaded C