When David Cameron tried and failed to derail the eurozone’s new fiscal compact a couple of years ago, Nicolas Sarkozy was exultant. The British prime minister found himself isolated at an all-night sitting of European leaders in Brussels. By the account of another of the leaders present, the then French president all but punched the air in delight. For Mr Sarkozy “40 years of hypocrisy” in Britain’s European policy at last had been exposed.

These days the insults are being hurled across the Channel in the other direction. Mr Cameron has decided that France’s economic troubles will serve him well in Britain’s 2015 election campaign. François Hollande, Mr Sarkozy’s Socialist successor in the Elysée, is held up by Downing Street as a warning to anyone contemplating backing Ed Miliband’s Labour party.

Vote Labour, the prime minister’s not-so-subliminal message goes, and booming Tory Britain will end up like stagnant Socialist France. Mr Hollande is not amused.

This is a silly game, though one sadly that offers a fair reflection of Mr Cameron’s careless approach to foreign policy. Britain and France, the only two nations in the EU that want to hold on to global relevance, are supposed to be building a strategic defence alliance. Mr Cameron is not about to allow anything so trivial to get in the way of firing cheap shots at the president in the cause of re-election.

The British and French have been loving, loathing and sometimes fighting each other for centuries. Even when they have been on the same side during Europe’s big wars, as during the first half of the 20th century, mutual interest has never quite dispelled mutual suspicion. French exceptionalism collides with British, well, exceptionalism. The centuries-old compulsion to compete is overlaid with marked differences of style and temperament.

I caught something of this the other day at a private gathering of the two countries’ political and business elites. The British, by and large, are po-faced and pragmatic; the French passionate and ideological. The inevitable gossip over drinks about Mr Hollande’s nocturnal scooter excursions – apparently the talk of smart Parisian hairdressing salons for more than a year before the story broke in the press – was a reminder the French are serious about sex, while the British are more comfortable sniggering about it. On weightier matters of state, Mr Hollande is thoughtful but indecisive, Mr Cameron self-confident but shallow.

There are points of convergence. The British revere the Queen; Republican France has more of the pomp and deference of old-fashioned monarchy. The British enjoy French food, the French have a taste for Britain’s less statist society. Both have expended blood and treasure beyond Europe’s borders.

The long tradition of rhetorical jousting also hides a truth that neither wants to confront. Britain and France are in the same boat; and it is slowly sinking. Tough times at home mirror shrinkage abroad.

The shared dangers are hidden behind short-term divergences. On the face of it, Mr Cameron has something to boast about. The UK economy is growing by between 2 per cent and 3 per cent, while France is stagnating. Unemployment on the English side of the Channel is 7 per cent, against 12 per cent on the French. London is filling up with smart young French professionals fleeing high public spending and tax.

Yet step back from the immediate and both nations face the same fundamental economic challenge. They are struggling to compete in a world where economic power is flowing to the rising states of the east and south. Britain needs to invest, France to reform.

France’s position in the eurozone – and more than that, the future of the eurozone itself – is put into question by a sclerotic labour market and burdens on business that suffocate enterprise and discourage job creation. Britain’s recovery is built on a housing boom and rising consumer spending. Even after a hefty devaluation of the pound, rising output is being mirrored by a widening current account deficit. France has a roster of world-beating companies; Britain does not make enough of the things the rising economies want to buy.

The view among French business leaders is that Mr Hollande’s latest plan to modernise the economy and reduce state spending should be taken seriously. They cannot be sure, and significant change has to wait for the European elections in May and the subsequent appointment by the president of a new government. But the consensus seems to be that the president has woken up to the truth that doing nothing can be more dangerous politically than confronting the guardians of the status quo. As for Mr Cameron, he can only pray that companies in Britain start to invest.

The two face the same harsh geopolitical realities. Both are nuclear powers and both have permanent seats on the UN Security Council. Both have mislaid their strategic anchors.

French political leadership in Europe has been ceded to German economic power. Britain’s effort to straddle the Channel and the Atlantic has been lost to rising Tory europhobia and diminished relevance in Washington. Relative decline was always inevitable in the face of the rise of the rest. The danger is of this hardening into absolute decline.

France and Britain will always find things to argue about. Yet neither has a map charting their course in a world that no longer belongs to the west. Perhaps they are more comfortable sinking together than collaborating. That would be a pity.

philip.stephens@ft.com

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