Les Arcs cannot claim to be the best destination for non-skiers. All is not lost, however. Here are some things to do if you are going to be in Arc 1800 for a week, and have some time to kill....
Take the bus to 1600 and then the funicular down to the market in Bourg Saint Maurice. The Grand Rue is quite animated, and the assembled stalls sell more cheese, ham and jam than you can shake a stick at. There's even a horse butcher. It starts at 8 and is over by lunchtime, so you'll need to be organised. After lunch you could have a swim in the municipal pool, which is on the road to Tignes and Les Arcs.
To the top of the Transarc to see the Grotte de Glace. This is actually quite good - each year there is a different theme. During November they create an ice cave, and then expert sculptors do their thing. The only downside is that the adjacent restaurant (La Creche) isn't Les Arcs' finest. But it's a good place to meet skiers and the view from the terrace looking over to the Nancroix valley is great. The Transarc is one of the lifts open to non-skiers (see below).
Snow-shoe walking. This "snow art" below the Varet lift (below) was created by a gifted snow-shoer, by the way. (Search for "Simon Beck" on Google to see his latest work). There are quite a lot of organised outings - Arc Aventures have a daily programme, as do the ESF in both 1800 and 1600. Some outings go from the top of the Tranarc; others in the forests above 1800 and particularly in the 1600/Courbaton sector.
Les chiens de traineau are not cheap, but it is an amazing experience. Their kennels have now moved from the Comborciere lift to Arc 1800, so the dogs can be closer to their clients. More here.
Check in at the Hotel du Golf. You can get good deals out of high season if you book direct. And they now have a small pool/spa complex which will be nice and quiet during the day.
Running out of options here, but today might be the day to take the bus round to Arc 2000 and meet your skiing chums at the Chalets de l'Arc (more on restaurants in Les Arcs here.) Pedestrians can (just about) make it to the Varet lift, and onwards to the Aiguille Rouge at 3226m).
If it snows or rains, the option of going to see a film in Arc 1800 and Arc 1600 is sadly no longer available. (The cinema in Bourg St Maurice on the main road is a listed building by the way). Occasionally some of the big blockbusters are shown in "v.o.", with English subtitles. Of course if you come before Christmas, you can immerse yourself in an entire film festival.
Connect with the "real France" by going back down to Bourg St Maurice and taking the train to Chambéry, which has a lovely setting, a fine old town and some good shopping.
Chambéry is, by some distance, the largest town in Savoie, is the capital of the department, a university town and one of the few places in the area to vote for the Parti Socialiste. More on the town here.
It is also home to a noted handball team, which regularly records attendances of 5,000+.
The tourist and lift pass offices sell a special "pedestrian guide", which includes one or two other attractions eg the "luge run", which goes from the top of the Transarc down to Arc 2000. A day's lift pass for pedestrians was €16.50 in 2011/12, with the following lifts on offer: Transarc 1 and 2, Arcabulle, Vallandry, Vanoise Express and the Funiculaire.