Use the cropdetect filter to determine crop parameters to remove the black. See Remove black bars using ffmpeg for an example of how to get the crop parameters.
Crop the black area and overlay the video over the image:
ffmpeg -i video.mp4 -i background.jpg -filter_complex "[0]crop=404:720:438:0[vid];[1][vid]overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2" -c:a copy output.mp4
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