We didn't do brunch, but enjoyed these 2 restaurants as recommended by a local friend: Deanie's Seafood (in the French Quarter) - has a GF menu & GF breaded fish. Cornmeal based. I did not get sick. I don't remember if separate fryer though... Also Mais Arepas, it's Colombian food and family owned. All GF naturally. Delicious! We took the Historic Trolley to get there.