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 is His slave and Messenger.
You have done well by repenting to Allah from this heinous sin; may Allah accept the repentance of both of you.
The marriage of the fornicator with the woman whom he committed Zina with before making sure that she is not pregnant is a matter of difference of opinion among the scholars; some of them are of the view that it is permissible while some others are of the view that it is void.
They also differed about the witnesses in the marriage contract whether or not trustworthiness is a condition in them. The majority of the scholars conditioned it while Abu Haneefa is of the view that it not a condition.
Since there is a difference of opinion and this marriage has already been conducted, and you have a child from it, then it is acceptable to continue this marriage without renewing the contract. This child is traced back to you in any case as long as it is not born before six months from the time you had consummated the marriage with his mother. This is whether or not you renewed the marriage contract, because in a doubtful marriage, the child is traced back to his father.
It should be noted that the witnesses of the marriage contract are all those who attended the marriage and heard the proposal and acceptance, so the witnesses are not restricted to only those who recorded their names in the register as witnesses.
Allah knows best.