Cheerfulflyer, please understand you will not be driven to FCT as it is a departures terminal only and has no provision to accept you from a connecting flight. You would as has been stated need to leave the airport and take a cab over to the terminal as though you started your trip from FRA. With this is mind, and as someone who did a C -> F connection in FRA, may I say that the FCL in the A terminal was completely delightful, met all our needs/expectations, and did include a private car to the aircraft where we were escorted aboard and introduced to the entire crew. It was a lovely experience and I don't regret not physically being able to use the FCT building at all.
Edit to add - we also had access to the FCL in ZRH (Swiss operated) and were driven from the FCL over to our aircraft privately as well. A nice amenity.