Have you ever heard of the Paleo Diet? It is a modern recreation of what mankind must have been eating before agriculture came into being. It may be an oversimplification to say so, but it is a variety of low Carb. No grains or dairy, just meats, vegetables, herbs, and fruit. There's no salt or processed chemicals either.
The people that lived here in the scrublands lived primitively in regards to diet, hunting and gathering and fishing. Following are some foods that it is thought they grew or encouraged to grow.
Maize, Beans, Squash, Pumpkins, Gourds, Citrons, Sunflowers
Here are plants they foraged for food, medicine, or weaving materials.
Acorns, Hickory nuts, Plums, Blackberries, Elderberries, Peppervine, Ground Cherries, Bristlegrass, Spatterdock, Yucca, Cabbage Palm, Water Lily, Rivercane, Palm berries, Wild Cherries, Persimmons, Blueberries, Huckleberries, Poke Weed, Amaranth, Broomgrass, Cattail, Ache, Morning Glory, Saw Palmetto, Yaupon, Smartweed, Knotted Bullrush, Nut Sedge, Buttonbush, Watershield, Sea Grapes, Coco Plums, Cofontie, Prickley Pear, Sea Oats, Goosefoot
They ate a wide variety of fish, shellfish, snakes, turtles, small and large game, and birds. These things Florida is flush with, as long as you know where to look.
Data from Ancient Native.