Henry II never *married* Alix de Porhoet. Site listed is crackpot. He did, however, chase every skirt that crossed his path, and caught most of them. (No wonder Eleanor was so vexed with him so much of the time!) Check this: https://fmg.ac/Projects/MedLands/ENGLAND,%20Kings%201066-1603.htm#H...
His maternal grandfather Henry I was even more notorious, and holds the probable record for known royal bastards (although no one has ever made an accurate count of Charles II's). This "Elizabeth Fitzroy" may have been one of them. Not cited at MedLands because no primary documentation, but that doesn't mean she wasn't.
I've not reviewed primary sources, but why is Elizabeth FitzRoy and not FitzHenry? Would it be Fitz Roi, as in daughter of the King? It seems Henry had several FitzRoy surname children listed... Wikitree has her as FitzHenry:
https://www.wikitree.com/wiki/FitzHenry-35
Martin "Braxton" Williams, III -- any of those would be correct, though in England the Fitz Roi version wasn't used. This isn't a real surname -- it's a thing she's called. If that makes sense.