Indeed, the former system (FNI - Fichier National des Immatriculations; Registrations National File) made number and thus plates to change when the car was changing department. But it gives an indication of the first registration of the car in a department, which can be useful for identification of the model year when it was the very first registration.
And it allow to see some mistakes

But with the 2009+ SIV (Système d'immatriculation des véhicules - Vehicles Registration System), the id is given for the entire "life" of the car : you don't have to change the number when changing department (but still have to declare it to prefecture ).

Et c'est très utile.

Mais un peu moins que ce qu'utilise dsl et d'autres pour les bagnoles britanniques, car (je me trompe peut-être) celles-ci reçoivent une immatriculation définitive, tandis que les françaises changent de plaque si leur propriétaire nouveau est d'un autre département.

It's quite a useful site, but a bit less than the tool used by dsl and others, since French car are newly registered when their new owner is living in another area, while the Brits are, as far as I know, registered once for life.

http://plaque.free.fr/

A French website mainly about plates from France, but also from some other countries.
It's not really user-friendly, with a new window/tab on each link (who told them the "target=_blank" was a "must to have" web gadget???), hurts eyes with the fancy colors and the gif pictures, has static data without research tool, but... is a gold mine about French plates from 1901 to present, with pictures, codes and dating.

(I think I'll propose them a php+mysql tool. It would be easier for our searches )
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There is an English version of the website (link on the top right of the main page) without the %@#µ! new tab on each link, but still with the gif pictures.
In practice, the tables remain in French, but the pages of explanations before are in English.