You will arrive in Terminal 2, United departs from Terminal 1. It takes around 10-15 min between the terminals by the Skyline train.
Check In deadline seems to be 60 min in FRA. If the plane is on time you should be outside of customs in 30-40 min. Normally you should be at the end of the United check in line around (or before) 9:50. Deadline is 10:20.
Doable if things run normal. What happens if you miss your United flight? Flexible ticket?