On the application for a Florida Concealed Weapons Permit, the section regarding criminal history, specifically states that "adjudication withheld" on a felony charge does not preclude eligibility. But, there must have elapsed, a period of 7 years (IIRC) since the final disposition of the case.
You will also be directed to attach a certified copy from the clerk of courts in the county where you were charged, regarding that disposition, to your application.
If you go to your local courthouse/tax collector's office, you can obtain a CWP packet, free of charge. It contains complete instructions inside...
Good luck.