Hi carolganz,
Thanks for coming out to Apple Support Communities for help with FaceTime on your new MacBook Pro and your external monitor. We're glad to help in any way we can.
To ensure we understand exactly what's occurring, please let us know more about the behavior you're seeing. Are you able to use FaceTime on your MacBook without issue when the external display is disconnected?
Do you see any kind of error message when attempting to use FaceTime with the monitor connected?
So that we're on the same page, what's the exact version of macOS installed? This can be found under Apple menu () > About this Mac.
If it's not yet updated to macOS 11.1, back up your computer data and update using the steps in this guide:
How to update the software on your Mac
We're here for you if you've got any questions. Have a great day!