Here are a couple of ideas that hopefully will be of some help. First, try going to http://louisdl.louislibraries.org/cdm4/document.php?CISOROOT... and see if you are lucky enough to find the version you're looking for digitalized. I believe they have 1872 and 1873 up so far.

If that doesn't work, the Richland Parish library in Rayville has a very large collection of microfilm of the Beacon. I believe that the LSU library in Baton Rouge may also have these microfilms available, but I've only used the one in Rayville while doing my lookups.

The Beacon was a fairly progressive and well managed paper for such a rural region. Best of luck!