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.
If this woman had married that man without the consent of her guardian, and no Muslim judge ruled that her marriage is valid, then this marriage is void because the valid marriage contract has some conditions, the most important of which is the consent of the guardian. For more benefit, please refer to Fatwa 83629.
Therefore, this marriage must be invalidated either by divorce or by a Muslim judge ruling that it is void. If that man does not divorce her, she should take her matter to an Islamic judge so that he would invalidate it.
However, such a marriage on which there is a difference of opinion has the same effects of a valid marriage in regard to tracing the children back to their father [the husband]. Therefore, if this woman is blessed with children with him, they are traced back to him.
For more benefit, please refer to Fatwa 92478.
Allaah Knows best.