A quick search for S. Louisiana lawns revealed this nice guide: http://www.lsuagcenter.com/NR/rdonly...esHIGHRES1.pdf
(edit: might be the same as the post above, if so, I endorse!)
Sounds like they only recommend warm season lawns. That's why the farm supply is saying it is a bad time. Warm season lawns are just that -- they need to be established in the warm season. So, Rye is a good cover for the winter until you wait for spring/early summer to establish a real lawn. As a matter of fact, the rye will look ridiculously good... It is just guaranteed to die about June 1. It will also grow really fast, so make sure you are ready to mow.
Meanwhile, do some research and find out what you have out front. Do you want the same for the back? You have some considerations to make. You'll also want to plan for preparing next spring (tilling, adding compost, killing off the rye, etc.)
I know in FL they love St. Augustine, but man that stuff is rough on the feet. Looks like you have a few other choices. Zosia, for instance, may grow well. That's finer and feels good.
Don't bother with the fine grained cool season lawns. They are nice, but only grow good up north. Sounds like your farm supply doesn't even carry them which makes sense.