According to this site, MCT at Frankfurt for international-to-international is 45 minutes. Which seems short. At the end of the day, if you want your luggage checked through, you will need to satisfy whatever MCT is in your originating carrier's system - so call CX and check what they think the MCT is. If it is any help, I have on one occasion had a connection, with luggage, which was less than the MCT (it may even have been through Frankfurt, but I don't recall), also on separate tickets, but the lovely F check-in staff at HKG (I am CX Diamond), after a minor flap, said they would override the system MCT restrictions and issue the luggage tag anyway, but were very clear in stating that the luggage might miss the connection and they were doing this at my own risk. Which was fine. Especially as it didn't miss, and arrived safely with me at my final destination (London).

If you aren't checking luggage, you can always get the second BP online. You should also try to link the PNRs (again, call CX) so they can try to protect the connection.