I was down there about five years ago and went to Bayou Burger on Bourbon Street because a burger sounded good and it came recommended.
They were the closest thing the French Quarter has to a sports bar. The Saints were not playing that day, but the Bears were playing Carolina (the infamous debut of Todd Collins). I threw the Bartender a twenty spot to turn that game on and he happily did so.
They had NFL network, so it is possible you could do the same. However, if any South teams are playing Saturday night...it might not be aired.
The burgers were quite good, so you can at least get dinner even if the game is out of the question.