You would have to be relatively high up or have a very exceptional snowfall to get snow.
The entire year, snow is always visible from the Aiguille du Midi. Many lifts in Chamonix are open in summer but not for skiing or playing in the snow. Most of the lifts serve hikers.
There may occasionally be snow patches in certain passes if you have a vehicle. Perhaps it will be the situation at 2500 meters on the north edges of the mountains, given how snowy this winter has been.
Chamonix had some of the most fabulous summer skiing in the Alps from the 1960s until the early 1990s. Due to the Grands Montets’ high elevation of more than three thousand meters, the long drag lift on the Petit Vert’s side operated all year efficiently.
On the Vallee Blanche glacier near Pointe Helbronner, a summer ski area ran in the 1960s. It featured at least three lifts and was run by an Italian business.
Unfortunately, the site’s security issues prevented this from continuing. The early 1990s saw the closure of these lifts due to high altitude, glacier movement, and the risk of crevasses.