A Muslim girl loves a Muslim boy, knowing it is haram in Islam, and also a big sin. If they get married will their sins be forgiven?
To have feelings of love toward someone (not mahram to you) without being married to them is not a sin by itself nor is it haram. But if those feelings of love lead you to commit actions that are sinful, then, of course, that's sinful.
Marriage to one another is perhaps the best solution if it is feasible. Marriage by itself may not be the cause of sins related to pre-marriage stuff being forgiven. Make the intention with Allah that you are getting married in order to avoid sin and gain the blessings of being married, and ask Him to forgive your sins in the past. And keep asking Him and returning to Him.