In reply to swiftvince:
I was there around that time last year (5-24 Sept). The weather was amazing for the first week and a half we were there, but was much more variable for the second half of our trip, with some lovely days and a few very wet/stormy days. However, overall it was very warm, even when wet.
Also, it's worth considering that it will be very much the end of the season by then. We were originally staying in Ailefroide which was already closing down for the season when we arrived (and all the buses had stopped the day before we arrived). We then had to move down to Vallouise for the last week, where most things were still open. However, some outdoor/hire shops in Vallouise were beginning to pack up for the season, so may be closed by the last week of September. The main alpine huts such as Pre de Mme Carle, Les Bans, and Glacier Blanc that you might want to hike to were all open and still serving food/drinks.
Everything felt very end-of-season, which was quite inconvenient for us as we didn't have a car, however, if you do have a car it could actually be quite nice. All the climbing and hiking was super quiet, we rarely saw other people on routes, except for the most popular sport climbs around Ailefroide.
Post edited at 18:25