I'd suggest you give some consideration to visiting the Loire Valley. Depending on your exact definition of Castle or Châteaux, the number there varies, but it's in the 25-50 range!
The best way to get to the Loire from Paris is probably to head to Gare Montparnasse and hop on a TGV. It takes about an hour to Tours, or about 1.5 hours to Angers, which are two of the big towns in the region which both have regular TGV services. That's towards the top end of your travel time, but not impossible. You can also drive - there's the A10 to Tours or the A11 to Angers. Driving would be quicker for getting around when you're there, but the TGV will beat the car hands-down for getting out there!
This question has some good suggestions on places to visit in the Loire, I'd suggest you start there for ideas.
If you want something more medieval looking, then the Château d'Angers (in Anger) was built as a fortress, with the main parts dating from the 9th and 13th Centuries. It's a formidable looking building, even today with the lovely ornate gardens that surround it! It's possible to walk around most of the ramparts, which offer stunning views out, and it now features a museum with a fine collection of medieval tapestries. It's a 10-15 minute walk from the main railway station in Angers, so you 1 hour 45 minutes after leaving Paris you can be stood inside!
Tours itself doesn't really have an impressive castle, but it does have a great Cathedral, and some large bridges across the river. There are two places fairly near by that have some great Châteaux. The first is the famous Château de Chenonceau. This is 20 minutes by train from Tours, and the station is just outside the carpark of the Château so you're there very quickly.
Another one fairly near by is the Château d'Azay-le-Rideau, that's about a 30 minute train ride from Tours then a bit of a longer walk. I've not been inside, only peered through the railings, but it looks pretty good from the outside! There are a number of other very nice ones too, but I think most of the rest will either need a bus, or will be outside your 2 hour limit.