Disputed. Perhaps for Latin *fignis, from Proto-Indo-European *dʰeygʷ- (“to stick, set up”), whence fīgō, or for Latin *fidnis, from Proto-Indo-European *bʰeyd- (“to split”), whence findō.
Other hypotheses include:
* From Proto-Indo-European *bʰeyH- (“to strike”); compare perfinēs (“(you would) break, shatter”).
* From the same source as Proto-Germanic *bainaz (“straight; ready”) and *bainą (“bone”), from Proto-Indo-European *bʰeyH-n- (“something straight, pole”), which may or may not be from the same root “to strike” above.
For the meaning “region”, compare pāgus again from a root meaning “to fix”.