10+ years of the Alps has taught me that looking at climate charts has nothing to do with the weather YOU will get on YOUR day.
It does show when you are most or least likely to have the weather you want, go and grab a dice from that monopoly set evryone has somewhere and roll the following to see how it pans out, one roll for each of your days.
Late May - Roll a 6
June - Roll a 4,5 or 6
July - Roll a 3,4,5 or 6
August Roll a 4,5,6
September - Roll a 5 or 6
For all other months you need to roll a 7.
I have been to that area in June, July and August, generally I have had good weather each time, I think most my Alps trips have involved the odd cooler day, the odd wet day and most have a few cool mornings, and f going for a long days riding the first pass of the day can be pretty chilly. But even when it is 30c in the valleys you might find the tops of high passes below double figures, and they can feel pretty chilly if it is overcast and windy.
Depends what you mean by "Summer Gear" if you are thinking of a trip of several thousand miles in a mesh jacket, jeans and trainers you are likely gonna be dissapointed - the odds of not being are similar to Euro-millions.
If you mean a summer textile suit with a set of waterproofs and a nice warm fleece you can put under it when its a bit chilly then Mid June to Mid September is likely to be OK and I personally would go for July, probably 1st half as slightly less busy.
I always wear a textil suit and take the inner liners, typically they are in for the first early morning run to the tunnel, and possibly across a bit of France, although last time it was high 20's before we even got on shuttle and 42c before the day was out, so they pretty quicky got thrust into bottom of pannier and stayed there for most of the trip, other trips they have remained in for most of the trip.
I find the outlast stuff very good so my suit is plenty warm enough with just a baselayer down to @10c, and not too hot until beyond 20c, this varies a lot with humidity 25c at the top of a pass can feel very cool, compared to the UK where a muggy 17c can feel pretty uncomfortable in the same gear.
The up / down nature of passes means the temp changes so often that a compromise outfit is fine, otherwise your putting your fleece on half way up each pass, then taking it off again half way down etc. This is where quality textiles are perfect, especially if they have good venting - mine is not great, but I just half open the front zip and loosen the zips on the ends of the arms to let air flow up them.