'assonantic' originates from English, formed from the noun 'assonance' + the adjectival suffix '-ic'; 'assonance' itself comes from Old French 'assonance', ultimately from Latin elements 'ad-' (to/toward) + 'sonare' (to sound).

'assonance' passed from Latin ('ad-' + 'sonare') into Old French as 'assonance' and into Middle English, and the modern English adjective 'assonantic' was formed by adding '-ic' to that noun.

Initially the Latin-derived element referred simply to 'sounding toward' or 'a sounding together'; over time it evolved into the technical poetic sense of 'resemblance or repetition of vowel sounds', which is the meaning carried by 'assonantic'.