No, a wedding officiant does not provide a marriage license.
You can get your license at the Clerk of the Circuit Court in any county in Florida. To obtain a marriage license you need: Identification: a picture ID such as a driver’s license, state ID card, or valid passport; both parties will also have to provide their Social Security numbers, but do not need to provide their Social Security Cards. Fees: $93.50.
Here is a good link with lots of info. Marriage Licenses – State of Florida.com: https://www.stateofflorida.com/getting-married-in-florida.aspx