Carcassonne and Surrounding Area

September would be better than October, on average, in the Bordeaux area.

Bordeaux is a bit of a drive. Unless you really like red wine, but then you can't drive (low limit in France).
An alternative would be the Dordogne area, Sarlat, etc.

The Cathars were very active in this area.

Some sites linked to Cathar history: Peyrepertuse and Querebus, south of Carcasonne; Lastours near Carcassone, and of course Albi.

September or October should be great, though note you will face diminishing daylight.

Maybe plan a night in Collioure after Barcelona, visit Peyrepertuse etc. enroute to Carcassonne. (After that I got nothin'.)

There are many, many abbeys in that area of France. Some are falling into ruin and others have been turned into wineries! Just google "abbeys near (insert name of town)" and you'll come up with quite a few.

Lourdes is only 2 1/2 hours from Carcassonne - well worth the drive if you are interested in Christian history. The pilgrimage site and the town are unique and fascinating. There is a lot to see and the evening candlelight procession is worth staying for.

This podcast discusses things to do in the area between Toulouse and Spain, excluding Carcassonne, which has its own episode (see below):

http://joinusinfrance.com/cave-paintings-in-france-around-foix-episode-48/

Here's one on Carcassonne

http://joinusinfrance.com/episode-23-carcassonne/

Here's one on Bordeaux

http://joinusinfrance.com/bordeaux-episode-44/

Here's one on driving in France

http://joinusinfrance.com/episode-16-driving-in-france/

The Pyrenean valleys west of Perpignan are beautiful; and they contain many sites which should be of interest to you, like the Priory of Serrabonne, the abbeys of St Martin du Canigou and St Michel de Cuxa, and the church in the village of Corneilla de Conflent. The medieval sculptures are amazing. The towns, like Castelnou, Vernet les Bains, and Villefranche, are much less filled with N. American tourists than places like Carcassonne.