Just to clarify what nyt was saying ... (From www.Service-Public.fr, the official French Government Administration website)
Justification d'identité
La personne soumise au contrôle a l'obligation de justifier de son identité. La carte d'identité n'est pas un document obligatoire.
The person who is stopped by the the authorities is obliged to prove his identity. An identification card is not an obligatory document
.... which I would interpret as being not being obligatory (ie the sole document required) because it can be replaced by another document if the person does not have one (ie not being a French citizen) or is a non-French national (most likely a visitor to France, or has not got their paperwork in order!!!)
L'identité peut être justifiée par un autre titre (passeport ou permis de conduire), une autre pièce (document d'état civil indiquant la filiation, livret militaire, carte d'électeur ou de sécurité sociale), voire un témoignage. Par ailleurs, une personne étrangère doit établir la régularité de son séjour en France (passeport, visa, carte de séjour).
The person can identify themselves by presenting another document (such as a passport or a driving licence)
(note that French driving licences have a photo, (often from way back when), a signature and an address) or another
(official) document (a birth certificate, military log book, voter's card or social security card) or be vouched for by another person present.
In addition, a foreigner must prove him/herself to be legally in the country in respect of his visit (by presenting a passport, a valid visa or a resident's card).
Si la personne contrôlée ne peut pas justifier de son identité, ou si les documents produits paraissent insuffisants pour établir l'identité (document sans photo), une vérification d'identité peut être demandée.
If the person cannot prove his or her identity or if the documents produced are considered insufficient as a means of proving his or her identity, further
(more detailed) proof of identity may be asked for.
The italics are mine to emphasize or interpret the French words to make them more comprehensible.
SO, if you are a non-French national, you should make sure you have a suitable proof of identity on your person when you are away from your accommodation, and nyt ... the Carte de Séjour is only provided nowadays if you really push for it as I had to when my previous card expired!!!