FitzRoy family

Yesterday, Ancestry.com sent me hints for Gryffudd ap Cynan, who is in the Reece family line. The Reeces have a wonderful Welsh ancestry. The name contains the Welsh "C"; they descend from Lord Rhys, ruler of S.Wales. While, looking, pursued a link to the English side, the FitzRoys. I had forgotten what the name means-illegitimate son of a king-when I turned a corner, and there was King Henry I, who was a son of William the Conqueror. Henry had 14 illegitimate children; one group used FitzRoy, another FitzHenry. Legit children used "of England" or D'Angleterre, since French was spoken until Edward III. Like most English, I have found numerous links to these Kings (Henry I to Edward III), but they were'nt English. The Perrys do not have a link.