What is the ruling regarding a young man who violated a girl's honor with her consent, and then regretted it after her family refused to marry her to him?

If what afflicted the young man was short of zina (fornication/adultery), then he must repent and cut off his relationship with the girl. It is not advisable for him to marry her unless she repents and shows signs of righteousness.

However, if zina occurred, then they have committed a grave sin. They must hasten to sincere repentance, which includes abandoning the indecency, cutting off the relationship, feeling remorse, and resolving not to return to it.

If they repent, Allah will forgive them. It is not a condition for the validity of his repentance that he marry her; in fact, it is not permissible for him to marry her unless she repents.

If the girl repents, then there is no objection to him marrying her; otherwise, he should seek someone else.