Ffraid Mair is absolutely right in Welsh.
Ffraid was a very, very popular saint in medieval Wales - just look at all the places called Llansanffraid / St Bride's.
Incidentally, Brigid, supposedly an Irish saint, is in fact a recycled Celtic goddess, which is really cool.
However, Ffraid runs a huge risk of being turned into Fred or Fried Fish or similar. I would love it to be used in Wales, but I can see why parents might not want to take that risk.
Mair is still used a bit - there's a TV presenter called Angharad Mair, and her second name is the Christian name meaning Mary, it's not the Scottish surname pronounced like "mare".
Again, the name the basis of all those places called Llanfair.
If Mair won't work, you could use Mari - short a, not Mah-ree like Marie Lloyd. Or Meirwen, which means Blessed Mary.