Visit the lake of Genova! It's close to Chamonix so it wont be a big extra journey.
Genova, Lausanne and Montreux are fascinating cities and the lake is one of the nicest in Europe. Jump on a boat or go swimming.
If you head about 50kms north you can add a visit to the Gruyère area. Very nice for hiking, cycling, hanging around small lakes, buying and eating chease directly from the mountainfarmers ...
If you are up for the sea, take the TGV from Paris to Marseille and visit the Mediter. coastline. Go to Monaco and St. Tropez, visit nice beaches and enjoy good weather!