For clarification:
16:9 footage is pillarboxed when turned into 4:3.
To letterbox would be to make 1.78:1 (16:9) wider - perhaps to cut it down to 1.85:1 or 2.39:1.
You should crop, rather than letterbox, and you should have shot the movie with the crop in mind. It doesn't necessarily make it look any more like a 'film', especially if you haven't framed specifically for it.