Thanks everyone for your replies.
Now I am really worried. The trip was puchased as a package with hotel. LH4063 FLR-FRA is scheduled to land at 4:15PM and UA 927 FRA-SFO departs at 5:25PM. At the time of booking, I knew nothing about FRA. I had thought a 1 hour connection should be okay. Since this was purchased as package, I am fairly certain I cannot change the flight on such short notice, at least not without significant penalty.
Upon further research, I have found that FLR-FRA leg of the trip is operated by Lufthansa CityLine, which uses terminal 1A. And according to United Airlines website, UA 927 usually departs from terminal 1A as well. Does this help matters, or makes no difference?
What should I do if I could not make the connection in time?