(1) It is unlawful for any person to own or to have in his or her care, custody, possession, or control any firearm, ammunition, or electric weapon or device, or to carry a concealed weapon, including a tear gas gun or chemical weapon or device, if that person has been:
(a) Convicted of a felony in the courts of this state;
. . .
[list of other disqualifiers]
So felons cannot possess any firearms, or carry a concealed weapon. But firearm does not include 'Antique Firearm' see below.
Note: Felons also cannot carry a concealed weapon...an antique pistol is a weapon. But they would be able to carry it openly because the open carry law only restricts the open carry of Firearms.
790.001 Definitions.—As used in this chapter, except where the context otherwise requires:
(1) “Antique firearm” means any firearm manufactured in or before 1918 (including any matchlock, flintlock, percussion cap, or similar early type of ignition system) or replica thereof, whether actually manufactured before or after the year 1918, and also any firearm using fixed ammunition manufactured in or before 1918, for which ammunition is no longer manufactured in the United States and is not readily available in the ordinary channels of commercial trade.
(2) “Concealed firearm” means any firearm, as defined in subsection (6), which is carried on or about a person in such a manner as to conceal the firearm from the ordinary sight of another person.
(3)(a) “Concealed weapon” means any dirk, metallic knuckles, slungshot, billie, tear gas gun, chemical weapon or device, or other deadly weapon carried on or about a person in such a manner as to conceal the weapon from the ordinary sight of another person.
(6) “Firearm” means any weapon (including a starter gun) which will, is designed to, or may readily be converted to expel a projectile by the action of an explosive; the frame or receiver of any such weapon; any firearm muffler or firearm silencer; any destructive device; or any machine gun. The term “firearm” does not include an antique firearm unless the antique firearm is used in the commission of a crime.
Also, if a felon is going to carry a replica of an antique firearm it must be an exact replica, same materials used in original construction, same sights, etc. Like if the original had ivory grips, some courts have ruled that plastic grips would make it not a replica and thus a firearm and illegal.