Ain't it funny how they Always seem to wait until you've finished patronizing their establishment (paid your money) until they decide it's important enough to approach? Write a respectful letter to Fazoli's corp and mention how poorly you were treated.
What are you required to do?
Nothing, unless you are asked to leave or specifically asked not to come back (possibly.)
Had you refused to leave then it could easily have been seen as criminal trespass.
What would I do? It depends on how addicted I am to Fazoli's (I love their breadsticks), I'd probably go back. If there is a problem just as "Are you refusing me service and asking me to leave?"
Get a name, or at least try to narrow down who the person could be described as and then raise a little helllloooo with that person's superiors. Most corporations like money enough not to turn it away UNLESS you are causing a disruption.