From Latin 'fari' (to speak) — literally 'easy to speak to.' Same root as 'fable,' 'fate,' and 'infant.'
From Latin 'affabilis' meaning 'easy to speak to, courteous, approachable,' derived from 'affari' (to speak to, to address), composed of the prefix 'ad-' (to, toward) + 'fari' (to speak, to say). The verb 'fari' is a direct descendant of PIE *bʰeh2- (to speak, to say), one of the most productive roots in the Indo-European family. From this same root came Latin 'fama' (fame, rumour — literally 'what is spoken abroad'), 'fatum' (fate — literally 'that which is spoken by the gods'), 'fabula' (a story, a tale), 'fabulosus' (fabulous — full of stories), and 'infans' (infant — literally 'not-speaking,' from in- + fari, because infants cannot yet speak). Through the Greek branch of the same root came 'phemi' (I speak), 'phone' (voice, sound —
The PIE root *bʰeh₂- (to speak) connects 'affable' to a surprising range of words: 'fable' (a spoken story), 'fate' (what has been spoken by the gods), 'infant' (one who cannot yet speak — in-fans), 'infantry' (soldiers too young/low-ranking to speak in council), and 'ineffable' (unspeakable). The power of speech runs through them all.