I just moved from BR about a year ago. There is a state owned range near Krotz Springs in the Sherburne Wildlife Management Area. It's about a 30-45 minute drive from LSU. You have to have a LA hunting lisence with the wildlife managament area fee paid ($15? annually). You also have to fill out a little form when you get there so they know that you're there. The game wardens come by every so often to make sure that you filled out the form, and there is a couple hundred dollar fine if you didn't. They have a rifle and pistol range, and two skeet courses (high house and low house), and maybe an archery range as well. The times that I have been out there it hasn't been too crowded at all, but I've heard that closer to gun season, it can get a little crowded.
I've also heard about some of the Parishes having sheriff department ranges that are open to the public, but I don't know if they would have a skeet course or trap range for recreational purposes or not.