Public bus transfers run from the airports to Les Arcs in the winter season, especially during weekends.
These transfers won't drop you at your door, but they are great value.
They stop at several places along the route and you may need to make a connection in Bourg Saint Maurice, where the funicular goes up to Arc 1600 (which takes around 15 minutes). From here you can take buses to Arc 1800, Arc 1950 and Arc 2000.
A bus also runs between the Bourg Saint Maurice train station and the villages in Les Arcs every Saturday in winter.
From Bourg Saint Maurice to Arc 1800, the bus transfer time is 30 minutes or 50 minutes to Arc 1600. It's a bit longer to get from Bourg Saint Maurice to Arc 1950 (1h10) and to Arc 2000 (1h45) by bus.
You can find the latest bus timetables on bus services in Les Arcs.