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...
(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. :-/)
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).