You might of course say "he is a Frenchman" or "she is a Frenchwoman", but you'd be more likely to say"he is French". (If you say "he is Frenchman" it,d sound as if were making out that you were Russian, because the Russians don't use article like a and the.)

English has all kinds of oddities about what you can say, and also about what you shouldn't say. So you can say "Yorkshireman" or "Lancashireman", but you can't say "Irelandman". And while it's grammatically fine to say "Chinaman" it tends to be seen as disrespectful.