Excited that you have the facial recoginition part sorted 
that is the hard part done.
One potentially quick fix I have depends on whether you have a Pull-Down Relay (Relais) or a Pull-Up Relay. Potentially by swapping your GPIO.LOW and GPIO.HIGH in your current code may fix the issue straight away.
With code there are always many different ways to solve a single task. If you arm yourself with similar examples I find a good solution usually presents itself. I’ll link you to a video using the same facial recognition software as us but altered so that it can control a Solenoid in a similar manner as the way you want your Relay to function (Code edits at around 4:26). Face Recognition Door Lock Using OpenCV on Raspberry Pi - YouTube
Hopefully, you will be able to frame and create working code from the above, if not pop me a message again! Would love to see a success photo if you do.
