I'm not sure how you would say it in the French language, but, while both are technically correct, "Frenchman" sounds a bit negative to me. I would ask, "Are you French?" :-)

Between those two options, "Are you French?" sounds more natural. However, "Are you from France?" sounds even more natural than both.

We use "Frenchman" to emphasise more on a person of French birth or nationality while "French" is used when emphasising more on the collective population of France. So, depending on what you emphasise on, your first question asks if he is one of his countrymen of France while the second poses the question of his individual nationality. I agree that "Are you from France?" would sound less intrusive as a conversation starter than asking "Are you a Frenchman?" probably as it asks of a country instead of a personal identity. Hope this helps. Lance

'Are you a Chinaman?' nowadays sounds dated and somehow a little aggressive. It's preferable to say 'Are you Chinese?' or 'Are you from China?' It's the same kind of thing for 'Are you a Frenchman?'