Perhaps he discovers some secrets about the wizarding world or Hogwarts that put him in danger. And he believes that Sirius, with his experience and knowledge outside of the school system, can help him figure out what to do. Also, the connection between them as godfather and godson makes Sirius a natural person for Harry to turn to when he feels the need to escape the situation at Hogwarts.
In some fanfictions, Harry might run away to Sirius because he is frustrated with the lack of understanding from his friends. Sirius, who has been through a lot himself, would be more likely to listen and offer different perspectives. He may feel that Sirius is the only one who can truly empathize with his situation, especially when it comes to his struggles with the wizarding world's expectations and the shadow of Voldemort.
One possible reason could be that he feels unsafe at Hogwarts. Maybe there are threats from dark wizards within the school that the teachers are unable to fully protect him from. Sirius, being his godfather, represents a safe haven.
Maybe he wants to escape the constant danger in the UK wizarding world. Voldemort's followers might still be a threat even after his defeat, and France could seem like a safe haven.
In fanfic, one reason could be that he might feel constantly in danger at Hogwarts. With all the dark forces targeting him, he could think running away is the only way to keep his friends safe. For example, if Voldemort's followers keep infiltrating the school, Harry might feel responsible and decide to leave to draw the danger away from others.
Perhaps he runs away because he feels misunderstood. In the fanfiction, the other students or even some of the teachers might wrongly accuse him of something. He could be tired of constantly having to defend himself. Like if he was wrongly blamed for a serious incident at Hogwarts, and no one seemed to believe his innocence, he might just leave in frustration.
Maybe they run away because they are tired of the constant danger at Hogwarts. They've faced so many threats, and they just want a break. So they run to a peaceful place where no one knows them.
Perhaps in the fanfiction, Harry Potter runs away from Britain because he is disillusioned with the way the Ministry of Magic operates. There could have been a major event where the Ministry fails him or betrays his trust. Also, he may be seeking a place where he can explore his magic without the constraints and expectations that come with being 'The Boy Who Lived' in Britain.
One reason could be to escape the public spotlight. After the war, Harry is a hero and Ginny is his girlfriend. They might feel overwhelmed by all the attention and want a quiet life, so they run away.
One reason could be to escape the constant media attention and pressure that comes with being in the wizarding world's spotlight. Harry especially has always had the eyes of the public on him, and running away might be a way to get some peace.
One reason could be that he wants to escape the constant attention and pressure. After all he's been through, he might just want a normal life away from the wizarding world's spotlight. Maybe he moves to a far - off place where no one knows who he is.
She could run away because of a broken heart. Maybe she had a relationship that ended badly, and she needs to get away from the memories. In the process of running away, she could meet new people who help her heal and grow as a person. This type of storyline often explores the more vulnerable side of fem Tsuna.
One possible reason could be that he feels misunderstood by his family or friends. Maybe he has some secrets that he's afraid to share, and the fear of being judged makes him run away.