Well, in fanfiction authors often take creative liberties. It could be part of an alternate universe scenario. For example, if there was a different timeline where the wizarding families were arranged differently. Hermione might have been adopted into the Black family (Narcissa's family) through some complex set of circumstances, like a deal between two powerful wizards to protect her from some dark force.
Fanfiction loves to play with the established lore. It could be that Hermione discovers she has some sort of blood relation to Narcissa through a very convoluted family tree. Perhaps there was a secret affair between a member of Hermione's family and a Black family member generations ago. And through some strange magic and inheritance laws, she ends up being considered Narcissa's sister in this fictional world. This can add a whole new layer of drama and relationships to explore within the story.