After a river cruise, we will be going to Barcelona and want to travel by train. Any suggestions about schedules and cost? We know that there is no direct train.
About a hundred bucks. You'd have a change in Nimes. The long-haul TGV runs about every three or four hours.
To find schedules you can use the Bahn (German Rail) website, following Rick's tutorial: http://www.ricksteves.com/plan/tips/db_tips.htm
To find prices and buy tickets, you can use the French Rail site http://en.voyages-sncf.com/en/, or the new Capitaine Train, which people find easier to use and does not mark up tickets: https://www.capitainetrain.com/
On this route, prices will start low for advance booking and nonrefundable tickets, and go up sharply as cheaper tickets sell out. If you book early enough, you can even get first class for only a few euros more.
There is a direct TGV at 08:43. The SNCF site shows Perpignan for departure times requiring one connection.