Brig is the capital of the district of Brig in the canton of Valais in Switzerland. It is close to the Swiss-Italian border. The name Brig comes from Briva or bridge. The place of meeting in the town is the train station, which links it to other Swiss cities. A Train Ride From Geneva To Brig This is a nice train ride from Geneva to Brig in Switzerland (Europe). You can see the train driver`s view from the locomotive (Re460).