paris to nice to barcelona by train.

How long is the trip and how many stops do you hope to make?

The direct route from Paris to Barcelona takes about 6.5 hours and does not go via Nice. Nice is a separate destination, a detour that adds to your travel time. I would consider flying from Nice to Barcelona, unless you plan other stops along the train route.

Those long train rides are offer significant advance purchase discounts. Rick’s France rail travel page has the link and tips for buying “Prems” rate TGV tickets through SNCF (cheap, reserved, nonrefundable, available three or four months ahead of your travel date) to print at home and pay with PayPal. It may not work with US credit cards, unless you have an extra level of security set up.

See www.skyscanner.com for budget flights.

Paris to Nice is easy by train, so is Paris to Barcelona, both routes have TGV's (high speed trains). Nice to Barcelona is a slow route.
To get some sample times (but not prices), go to www.bahn.de and put in 'Paris', 'Nice' and a random time and date about 2 months in the future, and see what you get.

For "help on trains," a great source is The Man In Seat 61. For instance, here's his page on Paris to Barcelona: http://seat61.com/international-trains/trains-from-Paris.htm#Paris-Barcelona

From Paris to Nice, just follow use his page on London to Nice and go to his information for Option 2, via Paris (since you're not coming from London or Lille): http://seat61.com/France.htm#London-to-Nice-by-train