[swisstrains]

I'm sure that there are probably some scenic rail journeys on the French side of the border but as far as Switzerland is concerned you will first need to travel for about an hour to the lakeside towns of Vevey and Montreux. From here you can take the 800 and 1000mm mountain lines to such places as Les Pléiades, Rochers-de-Naye and the Montreux Oberland Bernois line to Zweisimmen.
The next place of interest is probably Aigle. From here 1000mm scenic mountain lines radiate to Leysin, Le Sépey, Les Diablerets and Champéry.
After Aigle comes Bex where there is another 1000mm line up to Villars and Col-de-Bretaye.
Continuing along the Rhone valley the mainline then comes to Martigny where there are mountain lines leading to Orsiéres, Le Chable and Chamonix (for Mont Blanc). The next junction is Visp where you can pick up the Matterhorn Gotthard Bahn for a very scenic trip to Zermatt or continue on to Brig where you can either ride on the BLS railway over the old Lötschberg mountain line or take the 1000mm Matterhorn Gotthard Bahn for a ride up into the mountains in the direction of Andermatt.