Julie, is any sort of mounting provision attached to the fish? Is it on a board? More description, please. In fact, it would be most helpful if you could post a photo of the back of the fish.
An acrylic box with a rustic frame makes good sense. If this guy is really proud of his catch, offer him an Optium Museum Acrylic box...filters harmful UV light, ya know.
Those UVacrylic boxes are nice. We just put a new one on a autographed Evander Holyfield boxing glove. The sig was fading.
Someone has a large fabric and ropey, almost macreme (sp?) like piece on sticks... kinda hard to describe. It's in a large regular plexi box with no back. Thin plexi, square cut edges glued together, hung from the top through holes and with fishing line. She doesn't know what to do and her husband hates the plexi box. She wants it protected. I explained that the current plexi box offers zero % protection. The husband said "SEE!"

I picked it up at their home, which just sold, and I'm storing it and several others for a few months until they move into a new place when we will look at all their artwork, rework the framing, and redecorate.
So, where I'm going with all this.... Maybe a good treatment will be the same thing I'm going to suggest for this piece. It would work if the fish is pre-mounted like Jim says, or if you can get someone to mount it. Visit the home where it will be hung and look at the space. If it works, suggest that a portion of the wall be painted an accent color in a square around the fish. I'll be painting the customers wall, if you want to go that far. All bets are off if it's paneling. The object gets hung directly on the wall. A frame is cut several inches larger than the fish and attached to the wall, coverering the edge lines of the accent color. The plexi box is attached with screws to the outside edge of the frame. It's a nice look and the frame only has to look good, doesn't have to be anywhere near shadow box depth because the plexi box takes care of that.
This will work for my customer because it gives the wife her plexi box and gives the husband the finished look he desires. I hope it can give you some ideas too.