Justine According to the author, Lumière is supposed to be located in the Jura, which is one of the French departments that, indeed, make up the Franche-Comté region. However, I'm not sure exactly where the village is supposed to be. The author mentions the Alps but to see the Alps from the Jura, you have to get pretty high on the Jura Mountains, which are north of the Alps. He also mentions the "Jura Alps" which might be his way to refer to the same Jura Mountains. The precise location of the village is a bit unclear but you were right in assuming it's in Franche-Comté.
Je Antonuccio If its in the Alps, it would be along the southeast border. The Alps divides Switzerland, Germany, France and Italy.