The French air force was in such a bad state that even Vichy couldn't do much with them. Check this out:
http://france1940.free.fr/adla/ada_may.htmlFirst off, the French didn't have any types that were really comparable to the German planes. Some approached them in speed or firepower, but nothing that combined enough of these to really be a threat to experienced German pilots. The French pilots did do some damage to the Luftwaffe, but not enough to be considered more than a hindrance.
I've calculated that the French fighter strength (not including bombers and a large amount of observation aircraft) of the French AF was only at about 60% operational strength when the Germans attacked. Some regions approach 70%, but this is still not a good level of readiness. Many French aircraft had yet to be fitted with propellers when the Germans attacked. Of the aircraft that the French did have ready to meet the Germans, about 578 in ETO, not many were really sent up and the bulk of the French AF was captured on the ground.
As rogerdee said, most of the captured French AF were used by the Vichy government to patrol their own skies (and maintain some illusion of French nationalism). They were especially used for coastal patrol from what I heard. As the war progressed, the Germans gradually became less trusting of the Vichy government. I've heard that the French units were eventually taken off flight status as German air operations over France increased in '43 and '44, but don't quote me on that. Some were also used as trainers or in other capacities by the Germans, as rogerdee also pointed out. I'll bet some made it to England during the Dunkirk fiasco, but I doubt they were ever sent on missions across the channel. They wouldn't have been any match for the Germans at all, and it seems more likely to me that the French pilots would have been absorbed into the RAF.
Anyone got other good links on this?