It could be that Remus blames Harry due to his own insecurities and fears. He might be projecting his own feelings of guilt or failure onto Harry. Snape's help in this situation could be a turning point. Snape might initially be reluctant to get involved, but then he realizes the importance of the truth. He could use his skills in magic and his understanding of the wizarding world's politics to bring the real story to light and make Remus see that Harry is not to blame for Sirius. For example, Snape could uncover some hidden magic or a secret plot that was the real cause of Sirius' situation, and not Harry's actions as Remus thought.
One possible reason for Remus blaming Harry could be a misunderstanding of Harry's intentions. In the chaos surrounding Sirius, things might have been misinterpreted. Snape, being the complex character he is, might help because he has his own motives. He could see an opportunity to gain some sort of advantage, like improving his standing with certain people, by being the one to clear Harry's name and expose the truth to Remus.
In some fanfics, Snape might help by using his knowledge of the situation. He could provide crucial information that clears Harry's name. Maybe he has some insights into Sirius' situation or the events that led to Remus blaming Harry that others don't have, and he decides to share that information to set things right.
Maybe Harry discovers something about his past, perhaps related to his parents, that only Snape can help with. Snape was closely associated with Harry's parents. He might know some secrets or have some information that could help Harry understand a family mystery or some hidden power within him.
Sirius often provides emotional support to Harry in fanfics. Since Harry has lost his parents, Sirius, being his godfather, fills that parental role to some extent. He might share stories about Harry's father, which gives Harry a sense of connection and pride. Also, Sirius's skills as a wizard, like his combat abilities, can be used to train Harry or defend him when he's in danger.
He might be initially shocked. But if they were just having a friendly chat or doing something normal, he would quickly recover and probably join in the conversation. Harry respects them both a great deal, so he'd be more curious than anything else.
A plotline could involve Sirius and Remus trying to raise Harry while dealing with their own personal traumas. Sirius with his time in Azkaban and Remus with his lycanthropy. They could also face challenges from the Ministry of Magic, who might be suspicious of their non - traditional family unit. And of course, there could be a love story arc between Sirius and Remus that weaves in and out of Harry's upbringing.
One reason could be to save him. Maybe Harry is injured during a battle or some sort of magical accident, and Snape, despite their differences, steps in to carry him to safety. For example, if Harry is hit by a dark curse and Snape, with his knowledge of dark magic, knows he needs to get Harry to the infirmary quickly.
Yes, there are such fanfics in the Harry Potter fandom. Some fans like to explore different relationship dynamics and create unique storylines where Sirius and Remus are Harry's fathers in a romantic relationship. These fanfics often play with the idea of an alternative family structure for Harry within the magical world.
One possible motive could be a conflict over their loyalties. Remus is a werewolf and has his own set of insecurities and allegiances. Maybe Snape discovers something about Remus that he threatens to expose, leading Remus to kill him in a moment of panic. For example, if Snape were to find out about Remus endangering students during his werewolf transformations and was about to report him to the authorities.
One possible reason could be Snape's sense of duty to protect Hogwarts students in general. Even though he dislikes Harry, he might put aside personal feelings to ensure the safety of a student in a dangerous tournament like the Triwizard Tournament. Another reason could be Dumbledore's influence. Dumbledore trusts Snape and may have asked him to keep an eye on Harry during this event.
Maybe in the fanfic, Snape is written as having some hidden, truly evil motives that Harry discovers, leading him to kill Snape. For example, if Snape was secretly working for a new dark force even worse than Voldemort.