I found This in the OED

babble: early 13c., babeln "to prattle," akin to other Western European words for stammering and prattling (cf. Swedish babbla, O.Fr. babillier) attested from the same era, some of which probably were borrowed from others, but etymologists cannot now determine which were original. Probably imitative of baby-talk, in any case (cf. L. babulus "babbler," Gk. barbaros "non-Greek-speaking"). "No direct connexion with Babel can be traced; though association with that may have affected the senses" [OED]. Meaning "to repeat oneself incoherently, speak foolishly" is attested from early 15c.