As a caveat, I am not a lawyer, but I do know the law. In the State of Florida, signs prohibiting the concealed carry of firearms by license holders are absolutely meaningless. Like any private property (your house, the local mall, Disney World, etc.), the property owner can prohibit firearms. Carrying a concealed firearm in those locations are not a violation of Florida law. If discovered, the property owner can ask you to leave as they have the right to prohibit the carrying of firearms on their property. If a Police Officer is called to the scene, and you refuse to leave at the officers request, you may be arrested for armed trespass.
If your firearm is properly concealed (as it should be), this will never be an issue. Carrying in areas in which the private property owner has posted a "firearms prohibited" sign is not...and I repeat...is not a violation of Florida law.
As per Florida Statute 790.06, (12) the following locations are the only places where a Florida license holder is prohibited from carrying.
790.06 (12) No license issued pursuant to this section shall authorize any person to carry a concealed weapon or firearm into any place of nuisance as defined in s. 823.05; any police, sheriff, or highway patrol station; any detention facility, prison, or jail; any courthouse; any courtroom, except that nothing in this section would preclude a judge from carrying a concealed weapon or determining who will carry a concealed weapon in his or her courtroom; any polling place; any meeting of the governing body of a county, public school district, municipality, or special district; any meeting of the Legislature or a committee thereof; any school, college, or professional athletic event not related to firearms; any school administration building; any portion of an establishment licensed to dispense alcoholic beverages for consumption on the premises, which portion of the establishment is primarily devoted to such purpose; any elementary or secondary school facility; any career center; any college or university facility unless the licensee is a registered student, employee, or faculty member of such college or university and the weapon is a stun gun or nonlethal electric weapon or device designed solely for defensive purposes and the weapon does not fire a dart or projectile; inside the passenger terminal and sterile area of any airport, provided that no person shall be prohibited from carrying any legal firearm into the terminal, which firearm is encased for shipment for purposes of checking such firearm as baggage to be lawfully transported on any aircraft; or any place where the carrying of firearms is prohibited by federal law. Any person who willfully violates any provision of this subsection commits a misdemeanor of the second degree, punishable as provided in s. 775.082 or s. 775.083.
You can legally carry in any mall...its not on the above list. You can legally carry in Disney World...it is not on the above list. The mall owner can ask you to leave. The Mouse can ask you to leave. You can ask a concealed weapon holder who is carrying a firearm to leave your home. Its the right of any private property owner. If asked, you must comply, or you then risk arrest for trespass, as the property owner has asked you to leave.
Hope this helps.