Mr Darcy is not a member of the nobility, in that he's not a peer. However, `aristocrat' was a more general term, which would probably include families like the Darcys.

I have a suspicion that the word `aristocrat' as opposed to `nobleman' came to be commonly used only with the French Revolution, but I'm not sure of this. I can't check at the moment because I'm away from home and I don't have my handy Oxford English Dictionary with me (it's not something that is readily carried about in the luggage.)