It can be done, although some of the assembly is gunsmith level, requiring expensive tools, and should be farmed out. You can get it built.
The underlying assumption is that a main battle rifle built for long range performance using ammo good out to 600m is appropriate for cutting down into a carbine for near PDW use. FN's answer was the Para. What you get for the effort is a long action carbine that weighs two pounds more than the intermediate assault rifles that universally dominate that application.
Weapons in the military are chosen in a process that analyzes the various engagement ranges and the nature of the target. That narrows down the cartridge and caliber quickly. In this case, 20 feet to 200m is well out of the medium machine gun cartridge profile. From there, the barrel length that's optimum for the range, then the type upper receiver, stock/furniture, and what necessary accessories come last.
A broad overview would show most guns selected or recently designed for that job use intermediate calibers, have closed uppers on the receiver with picitinny rails, almost universally use an optic, allow for stock length of pull adjustment for armored vest wear, and the option of rails to mount vision enhancement devices. One major need is ergonomic controls with ambidextrous ability.
That's how much carbines have progressed in the 50 years since the FAL was introduced - and it wasn't a carbine. That's not to say it can't be done, but the essential features won't be there compared to modern ones. It'll be similar to a tanker Garand, which isn't morally wrong - but not exactly the result some expect. The SCAR would be a lot closer.
