I'm not aware of any easy way to do that with Premiere Pro, but you should first find out what the target dimension is for the video. Then, create a new sequence from File » New » Sequence, and set this dimension. Make sure you use the same frame rate and pixel aspect ratio as the input sequence.
Then drag the video onto the sequence, and make sure you don't change the sequence settings:
Finally, in the clip's Motion settings, you can adjust it to move and scale it until the black bars disappear:
With FFmpeg, you can run the
cropdetect filter to automatically detect the necessary area for cropping:
ffmpeg -i input.mp4 -filter:v cropdetect -f null -
This call will print out a line for every frame, but you can stop the process with CtrlC at any time. Look at where it says
crop= and use these parameters for the
crop filter. So, if the
cropdetect filter prints out
crop=1280:720:0:0, you just use that below:
ffmpeg -i input.mp4 -filter:v crop=1280:720:0:0 -c:a copy output.mp4
Naturally, this will re-encode the video, with a little quality loss. You should try setting a higher quality if you want to retain the visual impression:
ffmpeg -i input.mp4 -c:v libx264 -crf 21 \
-filter:v crop=1280:720:0:0 -c:a copy output.mp4
The CRF is a quality setting for the x264 encoder, with sane values from 18 to 28. Lower means better, and default is 23. Vary the setting according to the quality you want, and check the x264 encoding guide for more info.