One route you can go is using the GIS map feature of the Vermilion Parish Tax Assessor. Find the area you are interested in fishing, click on the map to identify "land" owner.
https://www.actdatascout.com/Map/Index?countyId=22113
I have seen one of those VC maps, and it's pretty ambiguous. Don't quote me, but I believe the permit covers the marsh West of the Freshwater City Rd (Hwy 3147) and East of that Weir off Humble Canal.
If the area in which you're interested is located outside the permit area, then theres a good chance its private anyway...either Audobon, Mcilhenny, or Vermilion/Exxon Mobil
Bon Chance!