Here in Ponchatoula, and in Hammond, we have a place called Berrytown Produce. They sell from local farmers first, and I find their prices to be about half of grocery store prices. Not an actual farmers market, but pretty close. I'll be making strawberry jam soon.

Here in Baton Rouge we have one year round. Here's a list that might help.

Here is a link that might be useful: Louisiana Farmers' Markets (click on the Search button)

Well, if you really want to travel, Fayetteville Arkansas has a Farmer's Market that is equal in quality to anything you'd see in Northern California or Connecticut/Long Island. I only went on three saturdays, but the selection was enormous. The locals grow rare heirloom varieties. One day there were red, gold, and white raspberries (all picked that morning). Several people had their own heirloom apples. All four sides of the old town square are packed with vendors. I was there in early September. Pretty much everything is organic (though usually not certified).