Gruyères – What’s up with the “s”?

This is a snap of some houses outside of the medieval village of Gruyères:

The “s” at the end always confused me, so I finally looked it up. The village is named Gruyères, with an “s.” But it is located in a district called La Gruyère, no “s” in the Swiss canton of Freibourg.

The snow covered peak in the background is La Moléson, sort of a mini version of the more famous Matterhorn, reaching just over 2000 meters in height.