hi wiesiek,
the french regulations are quite different from various around the world. there are already 2 things we need to separate, within a dive structure, or out of structure.
For the diving out of structure, there is no actual "regulation", you can go and dive with a buddy... whatever organisation you come from.
For the one within a dive center :
CMAS affiliated are the only ones recognized by law, therefore if you dont' dive in a padi dive center as a padi diver, you'll probably be asked to do a check dive which they call a "certificat de competence" (certificate of competency) which is only valid in the dive center where it is done.
Else you can do your CMAS 1* or 2* equivalence, the 1* is just provided, but for that you need to pay a yearly fee for the club (FFESSM or french diving federation), and you'll have to pay for the cmas 1* card.
For the 2* there are a few skills to show, but it's minimal, and you can get an equivalency card for your AOWD card if you wish... this can entitle you to go diving within or without a structure, in autonomy (as if you were just chartering, basically, with the french rules) down to 20m or with a guide down to 40m.
other point, weavers and other type of documents are not legal in france and a good part of europe, and you will be asked to provide a medical certificate (normally in french) to dive centers to be able to dive there.