Definitely Miriam, though Mireille is nice as well. Btw, it's not quite pronounced Mi-RAY, the final sound is more "consonanty" (not sure how I'd trascribe it in English). I think she'd have often to correct the spelling and pronounciation of her name, in an English-speaking context.
I like the pronunciation of the latter, but I have a tough time looking at it and getting that out of it. So Miriam by default, which is a shame, because I dislike Miriam.