All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Zina (fornication or adultery) is one of the grave major sins and it is an immorality and an evil way as Allaah described it in the Noble Quran. Therefore, it is an obligation to repent from it. Please refer to Fatwa 86527 for information on the conditions of sincere repentance.
Also, you must beware of having an affectionate relationship with a non-Mahram woman as this is a great door to committing Zina and it is for this reason that Allaah forbade it; please refer to Fatwa 81356.
On the other hand, it is not an obligation upon the fornicator to marry the woman whom he fornicated with; rather, even if he wants to marry her, it is not permissible for him to do so before they both repent from this sin and before making sure that she is not pregnant from Zina. For more benefit, please refer to Fatwa 82718.
If she repents to Allaah and you wish to marry her, and your parents object to it, then you should try to convince them. If they are convinced, then, praise be to Allaah, and if they insist on refusing while they have no sound Sharee'ah reason for doing so, then it becomes permissible for you to marry her especially if you fear temptation because of being attached to her. However, after finalizing the marriage, you should try to please your parents and comfort them. For more benefit, please refer to Fatwa 153881.
Anyway, if you want to leave this girl and marry another girl in order to please your parents, we hope that you will be rewarded for being kind and dutiful to your parents.
As regards the statement that the Quran stipulates that if a woman commits Zina, she is obligated to only marry the man who fornicated with her, otherwise she has to marry a non-Muslim, then there is no basis for this statement in the Sharee’ah as it is neither mentioned in the Quran nor in the Sunnah of the Prophet . Indeed, the Quran explicitly states that it is not permissible for a Muslim woman to marry a non-Muslim man as Allaah says (what means): {And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you.} [Quran 2:221]
As regards the saying of Allaah (which means): {The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that [i.e. marriage to such persons] has been made unlawful to the believers.} [Quran 24:3], then its meaning is that if the fornicatoress persists in committing Zina without repenting, then none will accept her as a wife except a fornicator like her or a polytheist who considers Zina to be lawful. But this does not mean that it is permissible for her to marry a polytheist as this is forbidden as we have already clarified.
Allaah Knows best.