Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Before answering your question, know that it is forbidden for a man to establish relations with an alien woman beyond wedlock. So, you must sever this relation immediately and repent to Allah. You should call her to Islam in circumstances where there is no risk of temptation.
As for marrying this girl, if she becomes Muslim, we advise you to convince your parents to deal with her kindly and accept your idea. Otherwise, you could ask some trustworthy and pious people – whom they trust – to intervene in order to convince your parents. But, if your parents do not get convinced, then we advise you to obey your parents as their obedience is given priority to marrying a given woman.
On the other hand, there should be no relation between your marrying this woman and her becoming Muslim. In fact, she is asked to become Muslim. If she becomes Muslim, Allah will make her life easier and she may get a pious, good-mannered husband.
We supplicate Allah to ease your matters and give us and you the good that is in this life and the Hereafter.
Allah knows best.