What is the ruling on fulfilling a promise to propose to a girl, after learning that the relationship between the two parties is impermissible, and given that the doer currently knows nothing about the girl?

You did well by ceasing communication with this girl, out of fear of Allah. Do not pay attention to her blaming you, for fulfilling a promise is recommended, not obligatory, according to the majority of scholars. The Sunnah has guided those who love each other towards marriage. If you desire to marry her, then inquire about her from trustworthy people. If they praise her well, then propose to her guardian. If you do not desire her, or if her religious commitment is not satisfactory, then turn away from her and seek another righteous woman.