Welcome Barry.
You're in the right place to start the process of learning to drive a rear engined open wheel race car. We've had a couple of Skippyforums members who've done the F1 driving experience. One in France and one here when the F1 Experience toured the US a few years back. You might want to double check the no restrictions part of the opportunity you're looking at as it has been our observation that those cars are rare and expensive to own and maintain so the people who run that program don't just hand you a helmet and fire them up. The ones I've seen require you to first show competence in a lower power formula car and then allow some limited seat time in the real F! car. They keep a close eye on you, very much limit your seat time and quickly pull you in if you put a wheel off or start scaring them.
There is just no way anyone without lots of seat time driving a high powered high downforce open wheel car could step into a modern F1 car and understand how to safely put it near its limits. Is it a thrill to pilot one of those cars around a track under your own control? Sure thing... But going anywhere near its limits is quite another. Like anything the learning curve is steep and worth respecting.
You are absolutely right to start with Skip Barber, but do a little more investigation before going to France to make sure you know what you're going to get. Once you start driving the SB car you may find learning to drive that relatively low powered car a worthy challenge all its own.