Florida Statute 741.01 in part, states that the Clerk of Circuit Court acts as an agent for the State of Florida for issuing Marriage Licenses. Links to several of the local Clerks are included below.
Bay County: https://www.baycoclerk.com/other-services/marriage-license/
Escambia County: https://www.escambiaclerk.com/212/Marriage-Licenses
Franklin County: https://www.franklinclerk.com/records/marriage/
Gulf County: https://www.gulfclerk.com/marriage/
Okaloosa County: https://okaloosaclerk.com/customer-service/marriage-license/
Santa Rosa County: https://santarosaclerk.com/other-services/marriage/
Wakulla County: http://www.wakullaclerk.com/marriagelicenses.asp
Walton County: https://waltonclerk.com/marriage