What is the religious ruling regarding a girl who was engaged, then became attracted to another man, and her family is aware of this?

It is permissible for engaged couples to back out of the engagement because it is merely a promise of marriage. However, it is forbidden for a man to propose to an engaged woman unless the fiancée has withdrawn from her first engagement, or the first suitor has left her, as stated in the Prophetic حديث (Hadith). If the official engagement means the marriage contract (aqd al-qiran), then the woman becomes legally a wife, and it is not permissible to propose to her.