How can an atheist European girl be convinced of Islam, especially since she believes that Islam is a religion of terrorism, given the desire to marry her despite the current relationship being forbidden?

You must repent to Allah and sever the forbidden relationship, and beware of the devil's whispers that tempt you to persist in the relationship under the pretext of da'wah (inviting to Islam). Inviting a woman to Islam is a righteous deed if the intention is pure for Allah and sharia controls are observed. This task should be undertaken by a knowledgeable Muslim woman, or an elderly man of piety and experience in da'wah. Seek Allah's help in connecting her with someone suitable to invite her, and seek assistance from scholars specialized in inviting non-Muslims. If she embraces Islam and becomes righteous, there is no impediment to marrying her.