Simple, but with minimum modification:
ffmpeg -i "$INPUT_FILE" -pix_fmt yuv420p -vcodec libx264 "$OUTPUT_FILE"
Complex, but resizes the video and may better support odd encodings:
ffmpeg -i "$INPUT_FILE" \
-pix_fmt yuv420p -vcodec libx264 \
-vf scale=640:-1 -vf "pad=ceil(iw/2)*2:ceil(ih/2)*2" \
-acodec aac -vb 1024k \
-minrate 1024k -maxrate 1024k -bufsize 1024k \
-ar 44100 -ac 2 -strict experimental -r 30 \
"$OUTPUT_FILE";