The early Greek and Roman term for foreigner was “barbaroi”, meaning that they babbled in a strange language.
And it is from the root word “barbaroi” that the word “babble” come from.
Another possible contributory origin is the Latin word as barba meaning beard.
A Roman would visit the tonsor to have his beard shaved, and the non-Romans, who frequently wore beards, or barbas, were thereby labeled barbarians.