exceptionally vs exceptionally well

I unequivocally prefer the second sentence. A native speaker would be very likely to think that the first is ambiguous or unclear. "You speak French exceptionally": exceptionally what? Exceptionally badly? Exceptionally slowly? Exceptionally fast? With an odd accent? It could even mean "You speak French, which is unusual". A careful native speaker would add a clarifying adverb such as well, badly, clearly, etc, or even a phrase, e.g. "You speak French exceptionally well for a first year student", or "You speak French exceptionally well for someone who has never lived in France".

I was talking to a French lady in a train (in France) and she flattered me very much by asking if I was Swiss.

Maybe she thought you'd stashed a load of Nazi gold.

Or she was Berne-ing with desire.

Merci beaucoup

Quel bon compliment!