VLC will preserve the video's aspect ratio when showing a video in full screen. If the video source is encoded in 4:3 aspect ratio, VLC will add black bars on the sides to fill the screen without stretching.

If you have a video that is widescreen but encoded as 4:3 with black bars, you will end up with black bars on all 4 sides. Top and bottom from the video and left and right from VLC. You can go to Video menu and adjust Crop to remove the black bars. Set it to video's original aspect ratio or your display's aspect ratio and that should do the trick.

If you want a normal 4:3 video to fill the screen, you can stretch, crop, or do a combination of both. The control is in your hands.