No experience in the french Alps, but I am based in Zurich and have been out a few times.
TODAY the snow goes down to about 1,800m, BUT, we have finally made it into spring weather, so we are talking 25+ °C weather and a ton of sun. I expect June will clear up just about all the snow below 3,000m.
I have run into late snow on a few occasions, not on passes, and pretty high, but with trekking poles, good solid high sided mountain boots, some patience you can cross, descend, or glissade (aka slide like a little kid
) down whatever is there. I was a total newb and did fine. I think they will be clear in a few weeks, July should be fine.
My advice would be to call the huts you have reserved nights in, a day or two before you leave, and ask them what is up. They are the expert on conditions.
But, I think you should be fine. We have gotten a TON of late snow, but the weather is pretty hot, and it is melting surprisingly fast. Closer to, you could try posting in the european board, or PMing someone in the area also, but I would go for the hut wardens!