Keeping in mind european attitudes to carrying ID - in some EU countries there are formal and informal penalties if you don't have it - this is not especially far fetched.
But yeah, the previous card was ridiculously large.
However, police forces are allowed to ask anyone their identity without any reason, and if they can't justify of their identity, they can be detained by the police for up to 4 hours for verification, and Police may requires them to do a fingerprint scan: https://www.service-public.fr/particuliers/vosdroits/F1036
https://www.service-public.fr/particuliers/vosdroits/F11601?...
Also, the comparison is ridiculous.
However, ID is never controlled, and many live with OQTF (Order to leave the French territory).