Marrying a girl who was engaged to one's cousin

There is a girl whom my cousin was previously in love with. The whole family knew and since he was still studying, the family wanted to marry them once my cousin's studies were over. After a year, for some family reasons, my cousin left the girl. I know that girl and I want to marry her and she too wants the same. When my parents and the girl's parent came to know about this, they are telling us that this is not possible, my cousin won't like it, what other people will say, what elders will say etc. In my point of view, its more society and culture thinking. I wanted to know what Islam says about this? What is the view?