I have been pondering on this. It is my understanding that it's an English translation of the Dutch '''Kanaal'' which of course means man made waterway.
So how did the English Channel get it's name?
Because it's a channel and we're calling it by its English name which would be biased toward England. In France, it's called La Manche.
If you're asking for the etymology of the word "channel," it comes from the Latin for canal which is "canal."