France - Car Registration
Vehicle registration is carried out at the Prefecture de Police for your department. You must have the car registration document or certificat d'immatriculation, commonly referred to as cart grise .
The grey card is issued by the Préfecture. It contains the technical/legal specs of the car: id number printed on the frame and on the engine (VIN in 'American'), the number of people it can carry, the max weight allowed, max/min size of the tyres, max/min dimensions of the car, engine declared power, the ownership history etc.
Remember that if by any chance you change address, even remaining in the same city and the same department you have to file the request and the Préfecture will issue a new 'carte gris'.
You have one month before being liable.