First, your statement is not totally correct.
You can carry a weapon in your car in Florida, but it can not be easily accessible unless you have a legally valid, state issued concealed carry permit.
This means that without a license, you can transport a weapon in your trunk, glove box if hostered or locked, etc. If you are pulled over for speeding and have an accessible weapon in plain sight you might be arrested for carrying without a permit.
If you have a concealed carry permit in Florida, you can carry a weapon on or about your person.