Alf,
The FNAR in .308 has a 1 in 12" twist. I've read all over the place these guns are very capable of shooting MOA or better. They're most likely to do that with Federal Gold Medal which utilizes the Sierra 168 Gr. Matchking Bullet.
These guns are basically Browning BAR's that accept a large capacity, detachable box magazine. That rifle has always been a decent shooter. If you haven't tried it yet, I would for certain pick up a couple boxes of the Federal Gold Medal stuff, along with the Black Hills equivalent of the same stuff. Go on a nice calm day, and I'll bet those groups will tighten up considerably.
There is one other thing I would suggest, if the Gold Medal factory ammo doesn't do the trick. Make up some handloads using the Sierra Matchking in both 168 Gr., and 155Gr. Go with 42.0 grains of Varget for both. Use Match Primers, and trim the brass to minimum overall length. Seat the bullets no more than .020 off the lands, and DO NOT CRIMP. Single load each round directly into the chamber, letting the action slam shut good and tight on each round. Take time prepping the cases, being sure to inside chamfer the neck, etc.
Varget has a good mid range burn rate, and 42.0 Gr. of it is perfect for both of my Springfield M1-A's. Your FNAR should swallow them without a hiccup as well. This load will cycle your action without damaging your op-rod. In fact, it's listed as a load for the M1-A and M-14 Service Rifle. Semi auto .308's do not like slow burning powders, because they put too much stress on the action, by allowing it to cycle while it is still under too much pressure. This load also shoots one hole groups at 100 yards with both of my Savage bolt action .308's. A Model 10-FP, and a Model 12FT/R. So I know they're good to go with a 1 in 10" twist which both of those rifles have.
Seeing as your rifle has a 1 in 12" twist, keep everything the same as I described, except drop down to the 155 Gr. Sierra Matchking. It's a bit shorter, and should improve accuracy in that slower twist rate barrel. It has the same ogive as the 168 Gr. Matchking, so you shouldn't have to adjust your seating die to hold the same cartridge O.A.L. Let me know what washes out. I'm guessing that gun will tighten up like a virgin on prom night.