Christine, hi. The question you asked about what is a Carte de Sejour. My wife (French) has a Carte Nationale d'Identité , I have a Carte de Sejour (official name Titre de Sejour) which is the same thing for foreigners. Having lived in France on and off since 1962 I'm so used to having it that it's second nature. And it's very easy to obtain these days if you're an EU citizen, not like back in the 60s in Paris where you could spend days queuing at the Paris Préfecture just to get to see someone who gave you the forms to fill out. You then had to go back with the forms and proof of residence/income etc, queue another few days only to be told something "vital" was missing from the file. It took months rather than weeks.
The guy at the Lozere prefecture was none too keen to renew my carte ("you know you don't need this...") because it meant he'd have to do a bit of work. But I told him what I've said here, that so many people seem to have or to give themselves the right to ask for ID that I just find it's useful to have it. Has more of an effect than my driving licence. Not only that, it replaces your passport in EU countries. I once forgot my passport on a trip to the UK and even there immigration accepted it.
As for proof of income, I just showed him the letter my pension fund sends me each year telling me how much they've declared to the tax people here.
@ Valerie -- You're lucky. Try writing a cheque in a shop. They'll always ask for ID and, if it's over a certain sum. will usually ask for two different documents (passport and driving licence for example).
@Andrew Sure, I could use my driving licence but I just find it easier to show the carte and as I just said, I've had one on and off for so long I'd feel naked without it!