I moved to France back in 2003. Based on this I asked a question where in the EU, EU citizens need a resident permit.EU citizens need a resident permit. Back in 2003 I didn't need to do anything other then a local. My Dutch identification papers were considered equal to the French papers. This isn't the case in my current country of resident (Belgium) where I am obliged to cary a resident permit.
The best source for detailed information is the city hall. I went to l'hotel de ville in Paris, Place de l'Hôtel de ville. If you are located in Paris, for the location alone I would recommend going there. There is a specific department dealing with administration for foreigners, ask for “info de carte de sejour”.
Be aware that the response are not always “customer friendly”, but if you can see through the rudeness of the civil servant in question, the information provided is quite accurate.
If you are renting a place in France you also might want consult the CAF. They provide the “aide personnalisée au logement” or APL. This is a subsidy on renting. Not everybody is eligble, but they check if all requirements for foreigners are met. The added benefit of going to the CAF is that you might end up with some financial help in paying your rent.