This is a common misconception.
The front facing camera does not mirror the video it takes. It mirrors the display when you are taking it, so it looks like what you would see in a mirror. The saved video is in the correct orientation. This is done to aid in taking the photos and videos. otherwise taking photos and videos with the front facing camera would be a bit awkward if you are seeing on the screen the reverse of what you expect.
If the camera were to save the video as you see it in the display then it would be inverted.
You can prove this, by placing some form of text in the shot. The display will show the text inverted, but the saved video, will have the text in the correct orientation.
What you are seeing on the screen while you take the video is what's inverted, not the final result which is as the camera sees it and no there is no way to change this.