Richard FitzWilliam, 5th Viscount FitzWilliam (1677 – 1743) was an Irish nobleman and politician. He succeeded to the Viscountcy of FitzWilliam in 1704, and became a member of the Irish Privy Council in 1715. He was elected as a member of Parliament for Fowey, a rotten borough in Cornwall. Now, you’re probably thinking that Cornwall is a long way from Derbyshire. However, that was the beauty of rotten boroughs. You didn’t have to live anywhere near them.
It is possible that this branch of the Fitzwilliam family had come from Ireland and migrated north to Derbyshire where they put down roots. Being of Hiberno-Norman ancestry, they might have intermarried with another Norman family, the Darcys. So it is possible, if not likely, that Mr. Darcy is of Irish descent.