No, but they are made by the same company.
There is a cameo or two of Final Fantasy characters in the Kingdom Hearts games.
I, however, have only played the first Kingdom Hearts. It's a real time battle rpg, set in several worlds (as the game progresses) that have been in Disney movies.
This is a PS2 game though.
The story line is fairly typical, boy needs to save universe from bad guy, but the hook of the game is the Disney tie in. Things like going into the world of Wonderland for quests and fighting along side Donald and Goofy.
From my experience, I enjoyed it, but didn't find it to be great.