All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu ʻalayhi wa sallam, is His Slave and Messenger.
If this man repents, then there is no thing wrong in accepting him as a husband. However, if he does not repent, don't accept him as a husband. In fact, some scholars even are of the opinion that the marriage of an adulterer to a chaste woman is invalid. Please, refer to Fatwa 89823.
The fact that he has a child born of fornication does not constitute a religious impediment to marrying him. It should be noted that according to the opinion of the majority of the Muslim scholars, the illegitimate child is attributed to his mother and not to his father as we have previously underlined in Fatwa 83408.
Some scholars, though, are of the opinion that the illegitimate child can be attributed to his father if he acknowledges the paternity. This view was adopted by Ibn Taymiyyah and Ibn Al-Qayyim . This applies to the case when the adulteress was unmarried; otherwise, the child is attributed to her husband because a child is traced to the owner of the bed (i.e. the legitimate husband).
Lastly, we would like to emphasize the importance of the Istikhaarah (guidance-seeking prayer) before marriage. Please, refer to Fatwa 81434 about the manner of performing the Istikhaarah prayer.
Allah knows best.