Did French yards retain carrier-building skills?

Did the other French shipyards still have the necessary skills after World War I?

Yes. France's cruiser program showed that four or five yards retained useful warship-building capability.

Industrial capacity and the decision to employ it were separate questions. France continued to distribute cruiser work across several yards, evidence that relevant shipbuilding skills had survived World War I. The facilities were neither identical nor equally efficient, although several could plausibly support large-warship or carrier construction with investment. France's choices about using and modernizing those yards set the practical limit.