Well, it's uncertain that "quarter" in this sense came from the Middle French. Early Modern English also uses "quarter" to mean "the relations between people",

Well, it's uncertain that "quarter" in this sense came from the Middle French. Early Modern English also uses "quarter" to mean "the relations between people", Shakespeare uses it for instance The actual link is obscure, but I don't think it matters too much - I'm observing a similarity, not attesting an origin.