The USGenWeb Project: Louisiana Archives, http://www.usgwarchives.net/la/lafiles.htm
can often be a useful place to find information. They have a "Louisiana Search Engine" plus individual web pages, often with a contact person, for each parish. I did a quick search on Henry Barron and did not find a marriage record, but I did not do a complete search using different possible name spellings. Even if you are unable to find the information on the site, perhaps the DeSoto contact person may be able to point you in the right direction.
The Louisiana Secretary of State site, http://www.sos.la.gov/tabid/638/Default.aspx
, has a searchable database of a tiny portion of the documents held at the State Archives. The database does not contain a state-wide marriage search, but it does contain a state-wide death records search which may be useful to you in the future.
The Le Comité des Archives de la Louisiane, Inc. is the non-profit genealogical support group for the Louisiana State Archives. Their website is http://www.lecomite.org/
. They may also be able to give you advice on how to proceed if DeSoto Parish marriage records are housed at the State Archives.
I have often found information using either the GenWeb or State Archive site when I was unable to find the information here on Ancestry.com.
Good luck with your search!