In reply to frictionlabs:
I presume you'll be going very soon, i.e. early Spring?
In which case the higher mountains are unlikely to be of great interest. There may well still be ski pistes open in Andorra but it's unlikely to be great so late in the season.
As others have mentioned, the valley climbing in Ariège will have everything you want and will be lovely this time of year. It's based largely around Tarascon-sur-Ariège, which is about 90 mins drive from Carcassonne.
Carcassonne castle ("cité") is worth visiting. The scale of it is impressive but I feel they could do more in terms of bringing history to life, as the presentation is fairly dry and uninspiring compared to some similar places I've seen in recent years.
A top tip would be to head to the edge of Toulouse, to the "Cité de l'éspace", which is a brilliant space museum (with an original Mir space station!) and is fascinating for adults and children alike.