Flumet has a free cross country loop around the frozen lake. You can walk down from the chalet in ten minutes. Equipment can be hired locally. This loop is quite short and is suitable for non-skiers who want a morning excursion or for those who like to finish off the downhill ski-ing day with a few energetic laps of cross country after the lifts close.
If you want a more serious cross-country experience, les Saisies has 120km of prepared tracks that were installed for the Winter Olympics. It is one of the highest cross country areas in Europe and is open until late April. Les Saisies is part of the Espace Diamant so if your party includes both downhill and cross country skiers, you can all drive over together (30 minutes). The cross country pass is about 10 Euro per day, but it's free if you have a standard Espace Diamant ski pass.