DISCLAIMER: I'm not a lawyer and everything I'm about to tell you is from memory.
The simple rundown is that any Florida resident *without* a CCW can carry a "common pocketknife" concealed. "Common pocketknife" is, of course, subject to interpretation. If you *have* a CCW, you can carry any knife concealed, including automatics (switchblades).
The ugly part is that, as I understand it, knife law in Florida isn't covered by the state preemption law that covers firearms. That means that communities around the state can pass whatever silly knife ordinances they want.
You'd be wise to get your concealed weapons license. Even if you never carry a gun, it offers you some advantages when carrying a knife, and it lowers many penalties if you do trip over the line.
"An armed society is a polite society." — Robert A. Heinlein
"After a shooting spree, they always want to take the guns away from the people who didn't do it. I sure as hell wouldn't want to live in a society where the only people allowed guns are the police and the military."
— William S. Burroughs