Earlier this week, Apple was having server problems which may have contributed to your issue. At any time, you can check https://www.apple.com/support/systemstatus/ to confirm that "FaceTime" and "Apple ID" services are online (they should have a green dot next to them.
If you continue to get the "unable to contact FaceTime server" error, check other apps internet-based on your device and confirm that they are working (send an iMessage in Messages, or open the App Store and install a free app). If everything but FaceTime is working, you may wish to contact Apple support at https://support.apple.com/contact
If several of your apps are failing, check your internet connection.