Have done that ride but it was 20 years ago in July. I think October if far too late! I know that
the following year other members of my cycling club did the same tour and they encountered snow and
freezing weather in July but when I did it the weather was glorious. So it can change.
If I could give you a few tips:
Don't even think of doing it in August as the whole of the continent is on holiday, hotels
are full and so are the roads. Surprisingly July is no problem.
I am guessing that you are Americans it may be cheaper to fly into London and then get a
Ryanair flight to Pau (West France) cycle across the Pyrenees and return to London from
Perpignan or Girona (east France/Spain). (Or of course in reverse of that). (Book well in
advance to get cheap flights).
We had no trouble at all in finding reasonably priced accommodation in July and I dare say
September would be the same. Just don't over pack and carry your own stuff - it gives you so
much freedom. Besides with commercial tours you have to do the days ride whatever - some
days you may not want to ride!
The scenery is magnificent, but those climbs are big!
Hope this helps some. (in UK).
http://www.ryanair.com/