In reply to happymarmot:
Try looking at some of the club reports.Most of our Alptreks have been one week,
This is our site with a few walk details archived, we tend to find September good for weather not been in June.
In reply to happymarmot: 2 weeks would be perfect for cham to zermatt "the walkers haute route" or the Tour de mont blanc.
the GR5 is tremendous start near nice and walk N or as Jon says start at lac geneve and head S. I bivvied it many years ago about that time of year. you can generally buy food every 4 days or so. don't bother carrying ice and crampons we posted them back after 3 weeks of dead weight.
In reply to Warner: Agree, the GR20 is special, but its not the alps and can become an ants highway as its very popular( for good reason). Best ive experienced in alps is the tour d'oisians around the ecrins. Could still be snow on the higher passes in june so you would need a walking axe to be sure of getting around safely. I did it during a similar time of year and hardly saw anyone else.
In reply to happymarmot: Go south. And don't rely on the season not being late - friends of mine abandoned a trek in June a couple of years ago because of substantial snow on the cols. So perhaps the Tour de Queyras, can't remember the number, or the Tour d'Oisans, GR54 round the Ecrins massif. The southern end of the GR5 should also be feasible, Mercantour etc.
In reply to happymarmot: If you're super ambitious try walking from Briancon to Menton on the Med - spectacular. It's the GR5 for a week then you take a right onto the GR20 through the Mercantour National Park. I'd avoid going to Nice - way too built up near the city - and instead take the variant to Menton. You're in pretty wild country virtually ll the way to the sea - we saw golden eagles + wild boar whilst looking down on Menton and along to Monte Carlo - stunning.
We did the GR5 from the N. to Briancon in a bit over 2 weeks and really enjoyed it. I have heard good things about the Tour des Ercrins too. Tour de Mt. Blanc was WAY too crowded, but that was in August.
In my alpine experience, Italian refuges are more comfortable and human, and have far better food than their French or Swiss equivalents (I've never been to Austria). Did the Alta Via of the Valle d'Aosta No. 2, which runs through the Gran Paradiso national park 3 years ago. Great experience, hard work though, as you cross from valley to valley each day. Did part of the Alta Via of Valmalenco about 10 years ago. The Marinelli hut is a stunning location.