You would not be at fault in this case. In cases like this, it's best to get all the documentation you can, like a police report. If you have comprehensive and collision, you should be able to get your car fixed.
Your insurance policy won't cover the damage to your friend's car — it's only your liability coverage that follows you as a driver. Since you're not at fault, I recommend that your friend contact the at-fault party's insurance to get the car repaired. Note that if the vehicle is uninsured but registered under your friend's name, the state of Florida can suspend his license once they check for insurance. If you have any questions, don't hesitate to ask.
Unfortunately, you likely won't be able to avoid any penalty for not having insurance. I would still recommend going to court with insurance — your judgment might be less severe if you resolve your uninsured status versus still being uninsured by the time your court date comes around.