A historic compromise with France is exactly what Britain needs

France and Britain can plausibly claim to have the longest-running national rivalry in the history of the world. With brief intermissions, the competition between France and England has been going on for nearly seven centuries, since the hundred years war. The very identity of Britishness, on which Gordon Brown is so keen, was forged in the 18th- and early 19th-century conflict with France. Britain invented itself as the anti-France.

This grand rivalry should continue for another seven centuries - on the football pitch and the rugby field. In politics, it has had its day, and must be replaced by a strategic partnership. Such is the proposition that President Sarkozy presented to Britain yesterday, with fire and eloquence, in what he wryly described as the world's seventh largest French city - London. We, the British, have never had a cross-Channel offer as good as this: an anglophile French president who is determined to add Britain to the Franco-German axis inside the EU; who is pro-American and ready to bring France closer to the military structures of Nato, not least in Afghanistan; and who seeks common ground for action on immigration, climate change, development and security. Britain would be mad not to seize it with both hands.

State visits are also about symbolism, sentiment and style - none more than this one, with Sarkozy's stirring speech to both houses of parliament praising Britain's wartime sacrifice for the liberty of France as well as British economic reforms over the past three decades, and conjuring a new Franco-British fraternité, an entente amicale in place of the old entente cordiale - not to mention the soap opera of Carla among the Windsors. But the essential argument can be made without a soupçon of sentiment, in the language of the cold analysis of power and interests that is one thing the French and the British have in common, and distinguishes them from most Europeans.

It goes like this. France and Britain were, in succession, the greatest powers in Europe. Both had empires; both pursued interests in most corners of the globe. Over the 20th century, the relative power of France and Britain declined in Europe, and the relative power of Europe declined in the world. Now, with the rise of China and India, the relative power of the west as a whole is declining.

At the same time, more and more developments that directly affect our vital national interests - climate change, energy security, pandemics, poverty in Africa, mass migration - are global challenges that no nation state is capable of addressing on its own. A group of states, such as the European Union, is perhaps the smallest unit capable of having a significant impact on them; and even then, only by leading the way to collective action with others.

For the past 50 years the European project has been mainly about Europe itself, from Franco-German reconciliation after the second world war to the reunification of eastern and western Europe after the cold war. For the next 50 years it will mainly be about what Europe does in its relations with the rest of the world, starting with neighbours who are not, in any likely future, going to become members of the European Union. In dealing with the rest of the world, the two most important European countries are France and Britain, precisely because they have the experience and speak the language of global power. If they disagree - as over Iraq five years ago - Europe does not exist as a force beyond its borders. Instead, France and Britain become the poles around or between which other states of a divided Europe align themselves. The result is a cacophony of impotence.

Even if France and Britain agree, Europe may still not exist as a force beyond its borders - that requires the engagement of Germany and other states - but it has a chance. Franco-British cooperation is a necessary condition, though not a sufficient one, for Europe to make a difference on any issue that matters in an increasingly non-European world. That is why we need a strategic partnership, a historic compromise, between Paris and London.

If you accept this logic, two questions remain: how can the theory be turned into practice; and are both countries really up for it? I'm more confident of my answer to the first than to the second. You do it by doing it. You go down the list of problems you face, compare your analyses, your interests and your available instruments, and see what can be done. Occasionally, the answer may be unilateral or bilateral. Sometimes, it may be joint action through the UN - where France and Britain are the two European permanent members of the security council - or through other bodies, including Nato. But nine times out of 10, the answer will have a European dimension. This may be the EU acting as one, or it may be leading European powers acting in concert - for example the "E3" (France, Britain and Germany) negotiating with Iran.

The French presidency of the EU, in the second half of this year, holds some possibilities, especially now that Sarkozy's Union for the Mediterranean has been turned into something half-way sensible. Next year the Lisbon treaty should make it a little easier to coordinate European foreign policy. If they choose to, Britain and France can between them shape the planned European foreign service, seconding their best officials to discover common solutions in areas where we have common European interests. But you have to keep at it, and you have to develop the everyday habits of cooperation, with the French and British working with each other at all levels of public policy. This is how the Franco-German special relationship has been built up, bridging what are arguably larger differences of worldview and foreign policy tradition. The exercise recalls Max Weber's definition of politics - boring holes through thick planks - but it can be done.

The real question is whether both countries are up for this. I fear Britain may not be. Had Sarkozy arrived with this offer 10 years ago, to a Tony Blair still fresh from his first election victory, it would have been a different story. But Brown in 2008 is not Blair in 1998 - neither in his personal instincts nor in his political possibilities. However, it's Sarkozy's fellow rightwingers on this side of the Channel who are most likely to destroy his vision. For on this question most British Conservatives are simply in denial. If you sit with them privately, they may grudgingly accept the logic of the argument I have spelled out. But politically they refuse to follow through to its logical conclusion: if you want to change the world, you have to work through Europe; and, as Sarkozy said in an interview with the Today programme: "If you want to change Europe, you need to have both feet inside it."

They will find this out in the end, after a few years in office, as all their predecessors did; but those years will have been lost, Sarkozy may no longer be there to tango, and the relative power of Britain, France, Europe and the west will be further diminished. The Conservatives are led by highly intelligent people, but on this matter - crucial to the future not just of this country - they are thoroughly earning their old nickname: the stupid party.

Timothy Garton Ash