Actually, this is quite simple if I understand you correctly.
You just have 2 action methods, The English one and the French one that load the same model in the same controller. However, if you have 2 names for the same controller, you could achieve this with routing configuration.
routes.MapRoute(
name: "FrenchControllerName",
url: "Home/{controller}/{action}/{id}",
defaults: new {area="Home",controller = "EnglishControllerName", action = "Index", id = UrlParameter.Optional }
);