Not that I know of. At least, for French citizens, within the scope of identity checks ("contrôle d'identité"), you need to be able to prove your identity but there is no required list of established means to do so (and some are not even documents, e.g., appeal to a witness): http://vosdroits.service-public.fr/particuliers/F1036.xhtml#...

The relevant article of the penal procedure code ("Code de procédure pénale"), 78-2, is especially broad: "by any mean" ("par tout moyen").

To my knowledge, the French state does not even require that a French citizen even requests or obtains an identity card or a passport (although having some ID document may be useful in practice).

From living in France, I always had the impression it was mandatory. All of my French friends thought it was bizarre that I would go out without my UK passport on me as they always kept their ID card with them at all times. My girlfriend's (whose French) parents never drive anywhere without ID on them (in addition to their driving license) and used to have a go at me for not doing the same.

All anecdotal though and maybe you're right that the letter of the law does not require it. The UK certainly doesn't.

I never had an encounter with the gendarmes in the 5 years I lived there so I never found out first hand.

Edit: looks like you're right. This article does a nice job of breaking it down: http://rue89.nouvelobs.com/2011/12/26/fouilles-controles-did...

What I said applies to French citizens, not foreigners. For foreigners the situation is less clear, in some cases you need to be able to show your passport and visa http://vosdroits.service-public.fr/particuliers/F31208.xhtml -- if you are within the scope of a visa exemption I would imagine that you would need to justify it by producing a passport of the correct nationality and supporting documents if any.

(Personally, I always keep my passport with me when travelling abroad.)

In France I always have my ID with me but I know friends who don't (e.g., did not bother replacing a lost ID). Having lived 24 years in France I have never been asked to produce ID by the police or gendarmes. (That said, I am white, not often involved in demonstrations and such, etc.; other people's experiences may vary. :-/)