In the Name of Allah, the All-Merciful, the Mercy-giving.

All praise is due to Allah. Peace and blessings be upon His Messenger Muhammad.

Zina (fornication) is an enormous sin. Fornicators need to repent sincerely to Allah and to earnestly ask for His forgiveness resolving to start a new period of chastity and purity.

They need also to increase their good deeds to wipe out evil ones. After mentioning a number of grave sins, including zina, and the severe punishment that awaits those who commit them, Allah out of His Grace said what means, “Except for whoever repents, and believes, and does righteous deeds. For [the likes of] them, then, Allah will substitute their misdeeds with good deeds. And ever is Allah all-forgiving, mercy-giving.” (Al-Furqan 25:70)

Regarding the validity of the marriage, Allah says what means “A man who fornicates shall not marry anyone but a woman who fornicates or an idolatress. And [as for] the woman who fornicates, none shall marry her but a fornicator or an idolater- and such [marriage] is forbidden for the believers.” (An-Nur 24:3)

There are different interpretations for this verse and therefore scholars have differed over the validity of such marriage.  However, there is no disagreement among scholars over the validity of their marriage if both fornicators repent sincerely to Allah.

Repentance wipes away sins and leaves a person as if born anew. But if they do not repent, the validity of their marriage becomes controversial.

As for the child legitimacy, you may, according to one opinion, register the child in your name as long as you deem it your child.

Almighty Allah knows best.