If you don't have the plates, the cop doesn't have to check anything. It is very visible that you don't have them. Doesn't France keep the registry of all cars

If you don't have the plates, the cop doesn't have to check anything. It is very visible that you don't have them. Doesn't France keep the registry of all cars and whether they have an insurance or not? I've just realized I'm not completely safe though, because — if what you are saying is true — someone from France can drive their non-insured car to my country and crash into me :)