One possible explanation is that you're wearing a hat that decreases rate of fire. The RoF stat for the Para 9 and FAL dictates how fast you can tap the fire button before jamming kicks in, so wearing such a hat can ruin those weapons for someone that's used to maxing their output.
A tip to completely get rid of jamming is to shoot the FAL at a normal speed twice and then shoot as fast as you can for as many bullets as you want. When you stop shooting, you'll have to do this process all over again. This works for me but see if it works for you.
That's odd. That used to fix it. Maybe a recent patch altered the FAL? Another possible technique which is very annoying but I believe still effective is to shoot twice without the scope and then zoom in and finish your kill. Not sure if this works though, it's a very old school technique.