Nothing good. He would obviously not be eligible to hold the office. Thus every law, order, etc, he signed would be illegitimate.
If he refused to "do the right thing", and the Congress refused to impeach and remove him, quickly. Then I think that the military would decide "it's time" to act on their oaths and "support and defend" the constitution against the "foreign enemy". (Assuming he was not a citizen at all, otherwise a "domestic enemy" if he's just not a natural born citizen), that he would have become. How ugly that got would probably depend on how long after he took office the revelation occurred. If he'd had time to get the next "Wesley Clark" into the position of Chairman Joint Chiefs, or into command of major unified or specified commands, it could get ugly indeed.
as mentioned - we’re screwed big time ... glad I live in the PNW - very sparse area - lots of forest - I’m a mountain gal anyway and can hold my own ... plus lots of us up here too.
That National Security Force thing scares the bejesus out of me ....