I have been to many of the places that you mentioned.
In my opinion, you would be taking on way too much for only two weeks, especially with two young children.
1) You are planning to rent a vehicle, make sure you have the right car seats. Also, sometimes renting a car in one European country and dropping it in another can lead to very high cost additions.
2) We did two weeks in Portugal with day trips into Salamanca and Santiago de Comp. and it was a full trip. We did a great Douro River cruise.
Also, you could easily spend a week in and around Madrid. I would not even try to do Barcelona, Madrid and Portugal in one two week trip, but it could be done. No way you can squeeze in the Basque country and southern France.
3) The weather will be chilly in November, especially if you go in the Pyrenees.
4) Either go with the Southern France, Basque region, perhaps adding Madrid OR Barcelona, or go with Portugal and Madrid perhaps adding Barcelona. There is a high speed train from Barcelona to Madrid. There is an overnight train from Madrid to Lisbon.