Hunting and trapping are allowed at the Barataria Preserve of Jean Lafitte National Historical Park and Preserve. The preserve is managed by the National Park Service. More information is available here or call 504-589-3882 ext. 119.
To hunt at the Barataria Preserve, a preserve hunting permit is required in addition to a valid Louisiana state hunting license. Waterfowl hunters will also be required to meet the necessary federal and state requirements, including purchasing duck stamps.
Barataria Preserve hunting permits are free and can only be obtained at the Barataria Preserve Visitor Center. Applications for preserve hunting permits are accepted at the visitor center Wednesday through Sunday, 9:30 a.m.-4:30 p.m. (the preserve visitor center is closed on Monday-Tuesday and on federal holidays). A hunter safety card is required (if applicable; all persons born after September 1, 1969, must complete a state-approved hunter safety program before being allowed to hunt in the Barataria Preserve.)
Check out the Louisiana Department of Wildlife & Fisheries for full details.