Oh, gee, how on earth can you tell the difference between FAY-lim and FAIL-im in normal speech? Very few people are going to make enough of a separation between the two syllables for this to be an issue. For the huge majority of people, these ARE the same pronunciation, and so they "come from" the same place.
So I'm sure both are "acceptable", though if you want validation for the way your prefer, that's how the name is divided in the pronunciation guide in Irish Names
OCorrain & Fidelma