Handbrake -- Smaller Video File Size or Converting Video
Handbrake is a free and open-source program that reduces the file size of videos, but keeps the overall video and audio quality.
It's technically video transcoder, letting you convert video formats and other options and such, but reducing video file sizes is what many, many people use it for.
Download it from here:
Once installed, click "Open Source," locate the movie file and select it, click "Add to Queue," and "Start Queue."
The bottom of the Handbrake window, between the "Save As" and the file name, and the "Browse" button, will tell you where the outputted smaller file will end up.
A notification will appear when finished to "Put down that cockatil...", and the converted video file will be ready, and will be a smaller file size.
If you don't like the result, click the "Preset" menu > "General" > "HQ1080p30 Surround," and then do the above instructions again. Rename the old or new ("Save As") converted movie file, or click to replace the converted movie file when prompted. This will make a smaller video file than your original still, but not quite as small as you first attempt, but with a better picture quality and audio quality.