Can I have a gun in my car in Florida?
Yes, and this was true even before permitless carry.
Florida law has long allowed a person to possess a firearm in a private conveyance where it's securely encased or otherwise not readily accessible for immediate use. "Securely encased" has a statutory definition covering things like a glove compartment, a snapped holster, a gun case, or a closed container requiring a lid or cover to be opened.
Since permitless carry, an eligible adult 21 or older may also carry concealed on their person in the vehicle without a license.
Where problems arise: vehicles that aren't yours, shared vehicles where the firearm's ownership is disputed, prohibited persons in the vehicle, and the constructive possession analysis when multiple people are present. That last one is the same framework that governs drugs in a car — knowledge and control, as to each person.
A firearm in a vehicle also interacts with any traffic stop, and how it's disclosed matters.
Whose car it is, and who else was in it, matter more than most people expect. ---
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