Which 3 months? I would go with starting in mid/late January, unless you want to enjoy the Xmas markets and decorations.
My personal preferences after several 3 week visits to Spain:
Madrid is a large city, not much in the way of "old town" vibe. There are 3 top notch art museums in Madrid, focused mainly on European painting, and a palace worth several hours. One of my faves was the Naval Museum. It is convenient for day trips. I haven't gone to any of the day trips you listed except Toledo and there I spent 2 nights. Toledo sounds like a place you would enjoy, with lots of medieval lanes and buildings and history. It is hilly (san-francisco-hilly). Going for a day would definitely short-change it. I would consider taking days from here for a 2-3 night stay in Toledo, and at least 2-3 more for another destination. I don't travel light, so I left my luggage at the Madrid train station and just took an overnight bag to Toledo.
It would be easy to spend a week or more in Sevilla, but it's not convenient for day trips. OTOH Cordoba is definitely worth several nights. It has the best preserved medieval center I've seen in Andalucia and it's a joy to wander in the evenings. There are lots of small museums to explore, focused on cultural heritage, history, gardens, and more. And there's the Mezquita!! I've spent 2-3 nights there and each time I left wishing I'd had more time.
7 days each in Granada and Malaga seem like overkill to me. I ran out of sights in Granada after 3 days and while I loved Malaga, there's not much to enjoy along the coast, if you're thinking of day trips. However, I would happily spend a week in Ronda with a car (I've done 3-4 days there twice) with day trips to visit other hill towns. I'd pick up a car in Sevilla and drop it in Granada.
I could see a minimum of a week in Valencia. I was there for a few days for Las Fallas - which was crazy with tourists and celebrations. If you are ready for an experience plan to be there around March 15-19.
I wouldn't take one day from Barcelona. There is so much to see and do and a dozen or more good day trips. Check out the options at the official TI website
France I haven't been to Montpelier or Avignon. My impression was that Avignon is better in spring and may be subject to the mistrals in winter. I did spend 2 days in Marseilles and enjoyed it much more than I'd expected, before moving on to Nice for almost a week in mid-March. Nice and the coastal towns were great, sunny, not too hot, not too crowded. It's easy to take day trips by train to all the towns along the coast from Cannes to Menton.