Unfortunately, by shooting in letterbox, you have recorded a 4×3 image with black bars on the top and bottom (rather than using the whole 4×3 chip and shooting anamorphic 16:9 which, when stretched using anamorphic interpretation, yields a 16×9 image.
The only way to do what you’re asking is to scale up your footage in a 16:9 sequence. Assuming this is DV, make a DV Anamorphic sequence and place your final edited movie (4:3) inside of it. It will display as pillarboxed, meaning that FCP will automatically put black bars on the left and right so that your movie displays correctly. It will also be letterboxed, since that’s how you shot it, so the image will be framed by black on all sides. Now, scale the clip up in the timeline until it fills the frame. Then, export as 16:9.
Since you’re scaling the image up, you may noticeably loose image quality. There’s no way around this, sadly.
Best,
Ben