The French used to bow. We gave it up for shaking hands. They replied by kissing friends on both cheeks. This need to differ is so instinctive that even when France and Britain begin to agree, they do so in such a way that instead of converging, they change positions.

One sees when it comes to the question of the integration of immigrants in French and British societies. Just as the British are beginning to see the weaknesses in multiculturalism, the French are taking to it.

The French tradition has been to establish as soon as possible that the newcomer is a French citizen in all dimensions. Religion, in the French experience, had been divisive. The notion was that religion was to be your private matter, not to be trumpeted in state institutions. It was illegal to state your religion in schools, on forms, in censuses.

Pride in France had never been affected by post-imperial self-doubt as it had been in Britain — and this included the 1968-ers. In schools immigrants were required to learn French history and there was a greater general strength of belief in French cuisine, French style and the French way of life.

In the UK the situation was different: empire guilt was associated with a desire to shake off the pomposity of the previous age, linked to the liberation movements of the 1960s. With it went the view that imposing British culture on others via the empire had been disastrous — we should encourage and learn from other cultures instead.

Imposing British culture on newcomers — many of whom had come from the former empire — would be considered similarly vainglorious. Notions of multiculturalism were born in this high-minded vein.

For different reasons, but at the same time, both the British and French are beginning to think that perhaps the other country had a point. The British are starting to realise that the problem with multiculturalism is that we may have emphasised the themes that divided people now living in the UK at the expense of the things that drew us together.

We may have been guilty of a different sort of racism in seeking not to share British culture with newcomers. The fact that a vast majority of Muslims do not feel as if they belong to Britain or it to them is a sign of the failure of multiculturalism. According to a poll, 81% of British Muslims believe themselves to be Muslim first and citizens of the UK second. The British have begun to draw up lists of Britishness in a faintly embarrassing non-British way. The British are urging each other to be prouder of, and more positive about, who they are. The British are, without recognising it, looking to the French.

The French have had riots, too, which made them believe that their policy of integration has also not worked: that there were thousands of alienated Muslims in the banlieues who had no conception of what it was to be French. Led by Nicolas Sarkozy, the interior minister, they have begun to think that perhaps les Anglo-Saxons have a point. Perhaps multiculturalism (or diversité) may have the answers.

They have set up institutions that parallel British ones. French politicians are turning to Muslim leaders to find out what Muslims think, instead of getting them involved in mainstream politics. Both have come to this position after violence against their societies. Both are in danger of throwing the baby out with the bathwater.

The French tragedy is that their principles are noble, but many Frenchmen are more racist than their principles. The idea that newcomers should be initiated more quickly into French society is a good one. The principle of the secular state is valuable in an age of religious diversity. But French immigrant populations are not being drawn into the mainstream culture because of a snobbery and rigidity that keep outsiders outside. Inflexible labour markets make it more difficult to absorb immigrants into that mainstream as well. It is not because French principles are themselves bad, but that they are badly applied.

The British, in contrast, may be so worried by the evidence that British Muslims have no sense of belonging in Britain that they seem to be all too prepared to accept the facile assessment that British Muslims are alienated by British foreign policy per se.

Whatever one might think of the Iraq war, it is simply incorrect to suggest that British foreign policy has been anti-Muslim, even in Iraq. If anything, quite the reverse: the wars in Bosnia and Kosovo were fought to ensure that Muslim societies could coexist in the Balkans; Saddam Hussein was a murderer of thousands of Muslims; the war to displace the Taliban replaced them with more responsible Muslim leaders.

The tragedy in the British case is that British Muslims are alienated by Britain’s perceived anti-Muslim bias. It is a tragedy of miscommunication. The British need to be firmer in pointing this out and in making Britishness more easily accessible to newcomers, as the French have done, while listening to some of the plausible complaints that immigrants may make about the problems in our societies.

Those voices would be better heard if those who did so do not feel the need to hide their faces — which is why Jack Straw is surely right to talk as he does about the veil. The riots and the bombs and the ensuing panic have both countries scurrying in the opposite direction. They should recognise what is good in their own experiences of integration, and borrow from the practice of the other where it can correct its weaknesses. Instead of changing places, France and Britain should be integrating their experiences.

The author is senior adviser to the Ax:son Johnson Foundation