If you start your trip in FRA, you will have the maximum F effect.

Pleasant check in via the FCT, skipping all the the extra security, shuttle directly to the plane.

If you start your trip in MUC, the ground service in F makes no sense.

Check in there is at an extra terminal (Building F), and no F doesnt stand for First Class. So no special F service there. The waiting room has more the feeling of a bus stop or train station.

After going through the security check you can ask for a limo pick up from the bus stop like waiting area to bring you to the FCL in Terminal 2 but then you have to go through security again before boarding the plane.

If you are connecting from another airport, I recommend to connect via MUC. You then can directly go to the FCL. Depending where you are coming from, you only have one security check, directly before boarding the plane.