From what I can remember, the falcons have an adjuster bolt in the trigger mechanism to limit the overtravel of the trigger blade after the sears have tripped. Sometimes this can work loose, causing it to engage before the sears have tripped and the rifle has fired; meaning at best the trigger seems really heavy, and at worst the rifle won't fire.
It's a long time since I've had a Falcon to bits, so this info could all be lies - try having the stock off and having a look - IIRC the bolt is near the rear of the trigger assembly