Acceptation is older than its synonym "acceptance"; it first appeared in print in the 15th century, whereas "acceptance" took until 1574. Grammarian H. W. Fowler insisted in 1926 that "acceptation" and "acceptance" were not actually synonymous (he preferred to reserve "acceptation" for the "accepted meaning" use), but the earliest meaning of "acceptation" was indeed "acceptance." Both words descend from the Anglo-French word accepter ("to accept"), but "acceptation" took an extra step. Anglo-French added the "-ation" ending, which was changed to form "acceptacioun" in Middle English. (English embraced the present-day "-ation" ending later.) "Acceptance" simply comes from "accepter" plus the Anglo-French -ance.
15th century, in the meaning defined at sense 1
Middle English acceptacioun, borrowed from Anglo-French acceptation, borrowed from Late Latin acceptātiōn-, acceptātiō, from Latin acceptāre "to accept" + -tiōn-, -tiō, suffix of action nouns