In reply to bjoe:
> I'm wondering whether mid-June would be too early for walking with no equipment in passes/tops higher than 2500m or not (say in Austria or in the French Alps).
I think not taking at least a small ice axe and crampons could spoil your enjoyment considerably at those heights in mid-June. You only have to round a corner on an easy trail between huts to find a small steep patch of snow covering the trail, still frozen iron hard in the shade after a cold clear night and perched above a 200m drop. With no equipment you may only have the options of waiting for it to get soft, or reversing your steps back to the hut.
All depends on where you´re heading for of course; the Austrian and French Alps cover an enormous area, and there´ll be huge differences in remaining snow cover depending on your location, the weather developments in the next 2 months, and on the general aspect of the proposed routes (N or S facing?)