I posted this question on a naval science newsgroup one time: Did US Navy aircraft ever engage the Luftwaffe during WWII? Nobody could give a definite answer, but the consensus was that it likely happened somewhere, sometime. I do know there was an American carrier strike on Norway early in the war. I don't know if the Germans came up to play though.
I'm sure it might have happened with some of the escort carriers, but the bulk of US naval power, and especially the strike carriers, were in the Pacific. If any US naval aircraft did take on a German, it was likely a Condor during a convoy escort. Using England as an unsinkable carrier, the AAF and RAF handled most of the airwork in Europe. On a sidenote, some naval fighters were given to the Royal Navy via Lend-Lease and did take on the Luftwaffe from Brit carriers.
Don't know for sure, but look into the history of the USS Ranger (CV-4). During her rather limited combat career her F4F Wildcats supported the Torch landings. I know that they engaged French aircraft, including some Curtiss-built P-36 Hawks. They may have engaged some German aircraft, too.
I think that some German Condors (Long-range, 4-engine recon/bombers) were engaged by our escort carriers and CAM ships. Mostly, the Condors were scouting for the U-boats, so nailing one of those must have been pretty satisfying, even if it did suggest that a wolfpack was in the vicinity.