Broken windshields are typically covered under the comprehensive coverage portion of a car insurance policy. Some states allow for the normal deductible to be waived for windshield replacements. Florida is one of these states, according to FL statute 627.7288 the deductible shall not apply to windshield damages.
The answer then is no, you should not have to pay the deductible for the comprehensive coverage used to fix the windshield. If your insurance company requests you to pay the deductible, state this statute or contact the Florida Department of Financial Services. You would have to pay for the damage if you don't have physical damage coverage.