How much to see, how many days do I need in Carcassonne and Avignon

Your 3 for Avignon, 1 for Carcasonne sounds about right. But do stay INSIDE the walls in Carcasonne for the best experience.

emi0504,
I love Carcassone, but one full day there is plenty. From Avignon you can take some easy day trips on 2 days and spend one full day in the town of Avignon.

I agree one full day each is plenty for Avignon and Carcassonne. I was in both places last October and stayed 2 nights, 1 day in each and felt I saw everything I wanted to see. Of course if you want to side trip from either, an extra day would be best.

We stayed several nights in Avignon and one night at Carcassonne. We arrived at Carcassonne late afternoon as the day tourists were leaving, and yes, stay inside the walls.

While we were at Avignon, we went over to Pont du Gard by bus, Nimes by train, and we took a half-day minivan tour of the beautiful Luberon villages the lavender processing shop, and the iconic lavender field in bloom.

If you don't have a car, be aware that there is no direct train from Avignon to Carcassonne. There will be at least one connexion (either in Narbonne or Nime).

I don't know for Avignon but I agree with the previous answers, no need to stay more than one night in Carcassonne, and since you are interested in history, also know that the medieval city of Carcassonne was largely rebuilt in the early 19th century in a "pseudo medieval" style, do not believe that everything you will see is authentic and dates from the Middle Ages. Quite the contrary, many architectural elements of the city are historical nonsense. So it's a bit like the Sleeping Beauty castle of our local Disneyland, it attracts a lot of people (and money). :))

The Cathedral of Albi located not far from there would be a more interesting destination, but if you don't have a car, forget it

Thank you all for your advice. I'm thinking of a day trip to Arles, which is close to Avignon? Do I need only one day for Arles?

There is a train from Avignon to Arles which takes less than 20 min. Cost is from around $6 to $45. There are also buses. They are less than 40 km apart. Easy day trips. Lots to see in Arles (e.g. Roman amphitheater and ruins, market, neat old town.....). I prefer it to Avignon.
Try to get to Nimes and the Pont de Gard (Roman aquaduct). Also not far from Avignon.

I personally find much more in Arles that's interesting than I do in Avignon. Avignon is IMO a place best visited via a river cruise. It loses a lot of its charm if you need to concern yourself with lodging and ground transport.