You can travel to the Alps by rail and particularly the Eurostar Direct service, which travels during the day. You can board in the UK at St. Pancreas Station in London or from Ashford International in Kent and travel direct to Moutiers without changing trains. Overnight services depart London on Friday evening and arrive very early Saturday morning (05h50), returning the following Saturday night. Daytime services depart London at about 10am on the Saturday, arriving between 17h30 and 18h00 in resort. 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.