Lately I have been getting into Endurance Running. If you are interested in this sport, Chamonix has 2 great races for you.
First in Spring there is the Marathon du Mont Blanc which is a mountain marathon with 2240 meters of uphill, run largely on trails (and only half that of downhill - it's a mostly uphill marathon).
Secondly in late summer there is the North Face Ultra Trail . This is a more advanced trail race, with entry requirements (it cannot be your first ultra marathon - you need to have completed at least 2 50K trail races or 1 80K or longer trail race to enter) and there are 2 race options - a huge effort in any case.
The CCC is the short one - only 90 kilometers and 4500 meters of uphill. The full Ultra Trail is 180 kilometers with over 9000 meters of uphill. The race is a running of the Tour du Mont Blanc walking path. They have time limits of 24 and 48 hours respectively.
If you are not running, you can watch the races from various points along the race courses, and also use it as an opportunity to go for a hike with the family.
Equipment: Check the websites for required equipment. The Ultra Trail requires you to be semi sufficient.