c. 1300, betrouthen, "to promise to marry (a woman)," from be-, here probably with a sense of "thoroughly," + Middle English treowðe "truth," from Old English treowðe "truth, a pledge" (see truth). It is attested from 1560s as "contract to give (a woman) in marriage to another, affiance." Related: Betrothed; betrothing.
suffix forming nouns of action from verbs, mostly from Latin and French, meaning "act of ______ing" (such as survival, referral), Middle English -aille, from French feminine singular -aille, from Latin -alia, neuter plural of adjective suffix -alis, also used in English as a noun suffix. Nativized in English and used with Germanic verbs (as in bestowal, betrothal).
<a href="https://www.etymonline.com/word/betrothal">Etymology of betrothal by etymonline</a>
Harper, D. (n.d.). Etymology of betrothal. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/betrothal