First of all, I'd like to reassure you that there was no widespread loss of records during the events that followed Hurricane Katrina in 2005. No genealogist should be hindered as all vital repositories are still available.
In Louisiana, each Parish Clerk of Court Office holds marriage records -- except Orleans Parish which is the Parish for New Orleans. As in many other cases, Orleans Parish is unique and the records of the Orleans Parish Clerk of Court can be found at the State Archives. Open records include all marriages 50 years or more (so up to 1956 or 1957 are probably available).
See their website and contact them. http://www.sos.louisiana.gov/tabid/88/Default.aspx