Both are conservatives; both are struggling to hold down government spending; both must reckon with anti-European pressures; both profess themselves defenders of national sovereignty. They even share a certain gastronomic populism: for Mr Major's fry-ups at Happy Eater read Mr Chirac's late- night pave with rouge at the corner brasserie. All this has encouraged hopes that there exists the basis for, if not quite a new Franco-British alliance, at least a closer understanding, and one that could be useful to Britain.
It was Mr Chirac's trenchant realism, the theory runs, that turned the European tide in Mr Major's favour in recent months. By placing national interest above European partnership and by taking one step back from the German embrace so long enjoyed by his predecessor, he altered the balance of the European Union. Interests are seen to be converging elsewhere. Take the nuclear tests in the Pacific. Britain, almost alone, has not condemned them. They are, we are told, a matter for the French. They, like us, are a nuclear power and that is burdensome. Mr Chirac must be grateful.
Yet this alliance is built on illusion. How did France respond to the outrage that greeted the first test? Not by stressing the independent, sovereign nature of its deterrent, but by suggesting that other European countries should or could shelter under the French nuclear umbrella. Perhaps this includes us. If so, what does Michael Portillo think about it? And what does he think about Mr Chirac's other ideas for European defence co-operation, which are to play an important part in today's discussions? For France, these are aimed at creating a European power to counterbalance the weight of the United States, an idea to horrify most Conservatives.
More importantly, on the future of Europe, London and Paris scarcely have a common approach - they may even be heading in different directions. Only last Thursday Mr Chirac was promising his people he would cut the public sector deficit within two years because, as he put it, "We must do it to be able to share in the single European currency". Is this scepticism? His words, it is true, may not be all they seem, for Mr Chirac has worn all sorts of economic clothes in his time, from free-spender to monetarist scrimper and from free-marketeer to dirigiste. Take his dedication to the franc fort: in 1986, when he became prime minister for the second time, his first act was to devalue. Or his views on taxes: during his election campaign he stated categorically that it was possible to cut direct taxation; in September his prime minister admitted that this possibility would not actually present itself for several years.
If nothing else, Mr Chirac's extraordinary performance in office these past five months should be enough to instil a certain caution on the British side. A mountain of difficulties on the international stage - nuclear tests, the franc under pressure, relations with Germany and Algeria - is matched by a similar mountain at home. An atmosphere of sleaze prevails; public employees and farmers are in uproar; businesses and consumers are squealing about tax. Last week even the chefs took to the streets: in the land of good food, they complained, a meal in a decent restaurant is now taxed at four times the rate of a burger in a fast-food joint. Little wonder that the President's approval rating stands at 14 per cent.
Mr Major may be justified in a sense of fellow-feeling with such a luckless, inconsistent and unpopular leader but that is no foundation for partnership. This is an alliance based not on any congruence of interests but on shared weakness. It is, perhaps, a model for the mean and shallow relationships that would exist in the minimalist Europe that Conservatives now speak of, but what sort of future is that? Mr Major and Mr Chirac are lost men clinging to each other in a storm; their embrace gives us little reason to celebrate.