Well, no.
You already have bills in your name, so there is nothing to do.
On the other hand, regarding ID cards (in France): First there is no obligation to keep the address on it up-to-date (so why is there even an address on it?). Second, if you do want the address to be up-to-date then you need to follow the administrative procedure to get a new ID card, which involves providing... a proof of address in the form of an utility bill!
> And proof of address is not a utility bill there, but either a form from your landlord or land register.
Because you've decided to do that, not because there is a practical requirement, which is my point.
Edit: because the decision was to have a strong ID system, so when people show an ID with an address the confidence is high in that being correct.