I suspect a "captured" French navy would have mostly languished in harbor as it was eventually scavenged for guns and other equipment for German shore batteries an the like.
A more interesting option woild be a Vichy French Navy that was allied with Germany. That would eliminate the problems of mixed armament and crews.
A more interesting option woild be a Vichy French Navy that was allied with Germany. That would eliminate the problems of mixed armament and crews.