Many thanks to Elizabeth who has left additional info in a comment!
According to background/extras requests, there is also some courtroom filming going on in St. Bernard Parish today and Mon-Fri next week.
If you are on the ground in New Orleans, that would be the historic courthouse in St. Bernard Parish. Info and location is here. If anyone is able to get over there and have a look, please report back – thanks.
Note: I am no† located anywhere near NOLA and am relying on the info of others.
Update: Many thanks to Joey for confirming that there was also some shooting at the courthouse yesterday.
Update X2: Many thanks to @luckyjohnson who has shared a photo that was taken on the courtroom set. It is here.