You’ll just need to do some math to figure out the new dimensions:
Your video is 1920×1080. It has an aspect ratio of 16:9. Meaning for every 16 units horizontally it is 9 units vertically. If a video was 500×500, it would have an aspect ratio of 1:1. If a video was 1000×500 it would have an aspect ratio of 2:1.
Your picture frame is 720×576 and has an aspect ratio of 5:4. You have an aspect ratio mismatch. Your picture frame is very close to a square shape, whereas your video is widescreen (almost twice as long as tall)
You can figure out the height that you need to maintain the 16:9 aspect ratio by:
1080 / 1920 x 576(picture frames height) = new height
It comes out to 405. So I would create a FCP project at 720×576 and drop your 1920×1080 footage into that. I haven’t used FCPX, but if it’s anything like FCP7, it should properly scale it to fit this frame with a letterbox on the top and bottom. You might need to put a black solid behind the video. You could try to just export a 720×405 from your 1920×1080 master, but I’m not sure if your picture frame will letterbox it or stretch the video to fit.
Good luck
References: https://andrew.hedges.name/experiments/aspect_ratio
Best regards,
Kevin Camin