What should a young man do who had an illicit relationship with a girl that involved touching and seeing 'awrah (private parts), and now wishes to repent and marry her, knowing that she does not love him, but her family approves of the marriage?

The conditions for repentance are to definitively abandon the sin, to regret it, and to have a sincere intention not to return to it, along with devotion to Allah. Therefore, sever your connection with the girl, and know that what you did falls under fornication, which is the share of the son of Adam. Repentance erases sins. Allah Almighty says: "O you who have believed, repent to Allah with sincere repentance. It may be that your Lord will remove from you your misdeeds and admit you into gardens beneath which rivers flow." And the Prophet, peace and blessings be upon him, said: "The one who repents from sin is like one who has no sin." Know that the best of women is the one who is religious. If you see that the girl might repent and become upright, then you may propose to her and marry her; otherwise, there is no good for you in her. It is not a condition for the validity of your repentance that you marry her; rather, if you repent with sincere repentance, Allah will accept your repentance.