The only marriage records that I know that are online are the ones for Orleans Parish (New Orleans), and they're not listed there.
If they didn't come to New Orleans to get married, I'd guess they stayed close to the base. Fort Polk army base is in Vernon Parish. Their Clerk of Court's website says you can do research in person, but also provides the link to the Vernon Historical & Genealogical Society which does lookups. http://www.vernonhgshistory.org/