Re: Lets just get on with it . . . .
he's applied for a "carte de sejours" (spelling?) which I gather is something like the UK Indefinite Leave to Remain.
A Carte de Sejour is essentially a residence permit, which fulfils the requirement for carrying ID when you don't have a French ID card. I got mine when I moved to France pre-EU, it was valid for 10 years. US citizens got one that was valid for 5 years. When I renewed mine the replacement had indefinite validity. My (British) wife recently tried to renew hers and was told that they weren't doing that now, because the government offices that issue them were short-staffed and they were too busy. It wasn't Brexit-related.
Overall it's not especially useful, since (unlike an ID card) it is clearly marked as not usable as ID for travel purposes, but it can come in handy when a bank or similar organization asks for proof of ID.