Double-decker TGV trains will soon be running direct between Paris and Barcelona. From 15th December 2013, high-speed trains will start between Paris and Figueres, Girona and Barcelona. From Paris Gare de Lyon, initially trains will run twice a day, increasing to four times a day in March 2014.
Information thanks to The Man in Seat Sixty-One. For more information, see: http://www.seat61.com/Paris-to-Barcelona-by-TGV-train.htm