Erik is likely not based on a true story. Many such characters are invented to entertain or convey certain themes and messages, rather than being rooted in actual happenings.
In fanfiction, Erik's possessiveness of Charles might be an exaggeration of his character trait. He may have a sense of ownership over Charles due to their shared experiences, like founding the X - Men together. His possessive nature could also be a way to show his intense love or loyalty towards Charles, in a rather extreme way. He might think that Charles belongs with him more than with anyone else, whether it's in their mutant - related activities or in their personal relationship.
In a different version, Christine gets lost in the opera house and Erik is the one who finds her. He could have been watching her from afar all this time. Instead of scaring her, he gently leads her to a safe place. They start talking about their dreams and fears. Christine realizes that Erik is not the monster everyone makes him out to be. This new understanding blossoms into love as they continue to meet secretly and share their innermost thoughts.
A simple fanfiction could be that Erik writes a beautiful song for Christine. When she hears it, she is deeply moved. She seeks him out to thank him. This encounter starts a series of meetings where they slowly fall in love. Their love is based on mutual respect for each other's talents.
It can start with conflict. Raoul is the 'good guy' and Erik is seen as the 'bad guy' at first. But as the story progresses, they could find common ground. For example, their shared love for Christine could be the starting point. They could have a conversation where they both admit their feelings for her and realize that they don't have to be enemies.
Another place could be Fanfiction.net. However, the search functionality might be a bit less precise compared to AO3. But it still has a large collection of fanfictions. You may need to dig a bit deeper and use more specific keywords in your search, like 'Erik x Charles slash' which is sometimes used to denote YAOI content.