Once Louisiana became U.S. territory in 1803, Protestant preachers entered the area and churches were begun. For Protestant church records, you would need to consult the individual churches or the repository for records for that church. For example, the United Methodist Church has an archives in Shreveport that contains some of the records from its churches in the 1800's. Baptist churches, which may be independent, may have kept their records at the church. Please remember that Protestant records are not nearly as complete as Catholic.
Documents filed in the courthouse often list family members and relationships.
There are often indices available that make it easier to locate someone. The courthouse is the repository for marriage records, successions, land records, and a variety of other records. Marriage records are the courthouse records with the most clearly relevant connection to genealogy. Sometimes they will have information that the church records doesn't. And sometimes, when the church record can't be found, the civil record is the only documentation available.