You're better off with Southern Home grapes, a hybrid of bunch grapes and muscadine grapes. My Concord grapes were susceptible to fungus with the high Florida humidity.

Or, pure muscadine/scuppernong types.

'Southern Home' is a known entity, but an accomplished grape grower once told me that it was really more of a novelty and ornamental than a good fruiting variety. Supposedly, there are much better muscadineXbunch grape varieties, but they don't have the notoriety of SH.
The late Bob Zehnder, of SC, IIRC, had developed a number of muscadineXbunch grape hybrids that were probably better than Dunstan's 'Southern Home', but I don't know if they're available in commerce, or if they were lost when he passed in 2007.

This discusses north FL grapes:
http://edis.ifas.ufl.edu/mg248

Here is a link that might be useful: The Bunch Grape (Florida)