ANSWER:
He is living in zina with this woman as a muslim man can only marry a muslim woman, or a chaste Christian or a Jewish woman.
He cannot marry a polytheist and he will be sinful if he did while acknowledging that such a marriage is invalid.
If he believes that the marriage is valid while being shown the evidences of the Quran, Sunnah and the consensus of scholars that such a marriage is invalid yet he still says it is valid, he is an apostate and his prayers, Hajj and Umrah are all invalid.