Loire Valley without a car
 

Would like to visit a chataux or two -
Plan to travel from Paris for 2- 3 days.

Is there a train ?
From where to where?

yes, I've gone to the Loire Vally by train.

From Paris, you can mainly get to Tours. Amboise and Blois (with chateaux) are also on the train route, but I don't remember if they are on the main route to/from Paris as I visited them from Tours, which was my base. You can also visit Chenonceau by train from Tours. Chateau visits are real popular in TOurs, of course, so there are lots of local tour companies that have day trips for those, and you can find info on them in the train station. It's just that some are not that convenient by train or bus, due to scheduling or where the station is compared to the chateau (eg, Azay-le-Rideau).

If I were you, I'd take the train to Tours and use that as your base for the 2-3 day visit.

Hard to do well without a car - since many of the chateaux are in the countryside with extremey limited public transport - unless you stay in Tours (icky) or Amboise perhaps and sign up for some local bus tours.