You can travel to the French Alps by rail and particularly the Eurostar Direct daytime service. You can board in the UK at St. Pancreas Station in London around 09H45 or from Ashford International in Kent and travel direct to Moutiers without changing trains arriving at approx 18H27. There is also an overnight service departing London on Friday evenings at approx 19H42 and arriving very early Saturday mornings (05h34), returning the following Saturday night late. There is no sleeper service on the Eurostar train.There is no sleeper service on the Eurostar train.
You can travel on a Eurostar service on any day of the week to connect with standard TGV services in France which will take you from Paris to the resorts both overnight in sleeper services and during the daytime. These services will normally mean a change of station in Paris and sometimes at Chambery or Lyon but do give additional flexibility with dates and times of travel.