In French the word banlieue [bɑ̃.ljø] can refer to:

1. Circonscription territoriale qui s’étendait à une lieue hors de la ville et dans laquelle un juge pouvait exercer sa juridiction.
(Territorial division that stretched a mile out of town and in which a judge could exercise jurisdiction).

2. Territoire et ensemble des localités qui environnent une grande ville.
(Territory and all the communities that surround a large city).

This word comes from the Medieval Latin banleuca (the space within a mile of a city to which extended the ban in feudal society). The word ban in this context refers to the jurisdiction of an overlord in which he could call vassals for war. It comes from Old French, from the Frankish *ban.

Sources: le Trésor de la langue française informatisé and Wiktionnaire

The word banlieue is also used in English to refer to “The outskirts of a city, especially in France, inhabited chiefly by poor people living in tenement-style housing” [source].

The English word banns, as in banns of marriage, probably comes from the same root as the French ban, but the English word ban (to forbid, prohibit), comes from the Middle English bannen, from the Old English bannan ‎(to summon, command, proclaim, call out), from the Proto-Germanic *bannaną ‎(curse, forbid), from the Proto-Indo-European *bʰeh₂- ‎(to say) [source].