I'm afraid I don't know that much about Belgian rifles...it's possible that you can find an FN Mauser action list somewhere of the serials. I don't know of anything off the top of my head. It's possible if you contact FNH, they may be able to help you (much like you can do for a Winchester or S&W). It's also possible that your rifle didn't start out with a sporting stock and could be a re-purposed military action (FNH started with a contract to build 150,000 Model 89 Mausers). I'd recommend trying to contact FN and see what they say; I suspect that any lists may have been lost in either WW1 or WW2 but it's possible them might still be around.
I think the original Model 1889s were in 7.65x53 and I'm guessinf the 7.9m mark on your rifle might be the caliber (so probably 7.92x57), so it's probably a later military model or a commercial action. Either was, send FNH a message and see if they respond and then just do some googling and see if you can turn up a serial number range list.