FonePaw Screen Recorder for Mac can record FaceTime video calls.
Step 1 Click on the FaceTime app on the Dock.
Step 2 Select Video Recorder on the Homepage of FonePaw Screen Recorder.
Don't forget to adjust the system and microphone sound.
Step 3 Select the recording area by dragging the dashed line box. You can make it perfectly match the FaceTime interface. Then begin your FaceTime calls while clicking on the REC button.
Step 4 When the video call is finished, click the red square button to stop.
You can preview the video or cut the unwanted part. Click Save to output the video call.
If you are not satisfied with the whole recording, click Re-record to record again. But the original video will not be saved.