All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Your marriage, dear brother, is correct if this woman did not have a husband because if she was married, then your marriage to her is void, as it is not permissible to marry a person who is already married. A woman can only be married once at a time. So if this man claims that he is the husband of this woman while your Christian wife denies it, then it is her statement that should be taken into consideration unless the man provides evidence that he is married to her and did not divorce her, and it is only the court which could rule about this.
Allaah Knows best.