Is it permissible to marry a girl who was previously engaged to another person after the engagement was broken off, knowing that she was not comfortable with her fiancé, and will God forgive the previous relationship?

If the girl accepts the suitor, then your proposal to her is forbidden, based on the saying of the Messenger of Allah, peace and blessings be upon him: "A man must not propose to a woman to whom another man has already proposed, until the latter marries her or gives up." However, if the girl does not accept the suitor (and she is an adult of sound mind), there is no harm in proposing to her; because the prohibition applies when the woman has accepted the suitor. The decisive factor in acceptance or rejection is the girl's word, as long as she is someone who cannot be forced into marriage. If the engagement is annulled, you may propose to and marry her.