Outside the ski season there are a whole variety of things to do: swim in the lake, go for walks, cycle, or read a book under a tree in the garden to the sound of cowbells. The swimming lake is perfect for children of all ages, and slightly older ones will especially enjoy the high wire course at Megeve and white water rafting at Passy.
There are plenty of village festivals and markets. Flumet has a small market on Tuesday morning. Many villages nearby have free outdoor jazz at weekends or choral concerts in the churches, and there are also horse fairs, antique stalls, and folklore festivals. The Megeve jazz festival and blues festival both have excellent musicians playing outdoors for free in the main square. It's not too crowded and suitable for all ages. Closer to home, in Saint Nicolas they close off the main (!) street one evening to install tables so you can relax with a glass of wine and a plate of aperitif while listening to jazz.
A typical day might be: more energetic members of the party walk down through the woods to swim in the lake before breakfast, bringing croissants on the way back, a leisurely morning around the house, lunch on the terrace, everybody go down to the lake for a few hours after lunch, then drive up the road above Saint Nicolas for a couple of hours walk in the hills. In the evening, if you're eating out, the walk along the quiet road to Saint Nicolas is very pretty, Chalet la Source is an excellent place to eat, and there's a good chance of seeing the local Chamois on the way (they normally come down out of the woods in the meadow just where the footpath to the lake turns off.)
Although July and August are the most popular months, Flumet can be even nicer in the Spring and Autumn as the weather in summer can be very hot. If you're planning long days out walking or climbing, May, June, September and October may be better.