What is the ruling regarding the children of a Muslim man who married a Jewish woman during the pre-Islamic era (Jahiliyyah) without a lawful contract, and now wishes to enter into a lawful contract?

A Muslim must repent to Allah from committing adultery, which is a grave sin. It is not permissible for him to marry an adulterous woman, even if she is from the People of the Book, because she is not chaste. Children born of adultery are not attributed to him, nor do they inherit from him.