FFTA has a new storyline, but I don't think it's nearly as strong as the story of the first. Basically, it's about this group of kids who read a mystical book and then wake up to find themselves in the medieval fantasy world the book was about. However, they've all been given different, mostly opposing roles.
For instance, the hero Marche has formed a new fighter clan (more like a gang, but legal) and uses his new group to survive in the world and hopefully figure out what's going on.