Looks like the French name for the English Channel is La Manche (The Sleeve) and many other countries follow this name. Whatever you think of renaming things, however, the policy of giving all the names for a place was a good one.
It's an ok policy. For example I don't want to see "Chinese Taiwan/Republic of Taiwan" when I view Taiwan on a map as an America. It's just Taiwan to me and I'm not concerned with what people from other countries call it.
Same thing basically with the English Channel. It's just the English Channel. I don't want to see a bunch of different names for it. If the French want Google to show it as La Manche for French people that makes sense.
And then there are European countries that just use a combination. Germany has 'Ärmelkanal' (literally: sleeve channel). If you can't make everyone happy, make everyone angry.