Perhaps in this fanfiction, Naruto's power is seen as a threat in Konoha. His connection to the Nine - Tails or his unorthodox ninja ways might not be tolerated. And Fairy Tail is a place that welcomes misfits. So, he gets banished from Konoha and finds his way to Fairy Tail. There, he could learn new magic skills and form new relationships, which would be a great twist on his original Naruto story.
Well, perhaps in this fanfiction, Naruto is banished due to a false accusation in his world. He lands in the Fairy Tail world and is seen as an outsider. However, his determination and strong will attract the attention of some of the Fairy Tail members. Erza, for example, might see his potential and take him under her wing, training him in the ways of the Fairy Tail magic while he also teaches her some ninja tricks.
Naruto would likely be very confused at first. He has a strong sense of belonging and has always fought for his place in his own ninja village, so being suddenly banished from the Fairy Tail guild would be a shock. He might try to plead his case and explain that he has done nothing wrong.
He would bring his unique ninja skills. For example, his shadow clone jutsu could be adapted into some kind of magic - like ability in the Fairy Tail world. His strong sense of loyalty and friendship would also influence the Fairy Tail members. He might inspire them to be more united and fight more fiercely for each other.
The main antagonist could be a powerful demon that has been sealed in the Fairy Tail world for a long time. Naruto's arrival disrupts the seal somehow, and the demon sees Naruto as a key to fully breaking free. The Fairy Tail members and Naruto must put aside their differences and combine their powers to fight this demon.
One possible reason could be that he was wrongly accused of a serious crime within the guild. Maybe some powerful and influential members believed he was a threat and pushed for his banishment. For example, if there was a string of mysterious attacks and Natsu was framed as the culprit due to his often wild and uncontrollable nature in battle.
Another reason might be related to Naruto's loyalty being questioned. In fanfiction, there could be a plot where an enemy tricks the guild into believing Naruto has betrayed them. The Fairy Tail guild values loyalty highly, and if they think Naruto has sided with an enemy, they might banish him. For example, if an enemy uses some sort of illusion magic to make it seem like Naruto has attacked a guild member, this could lead to his banishment.
Often, it could be because of a false accusation. Maybe someone framed Natsu for a crime he didn't commit, like stealing a powerful magical artifact from the guild. So, to maintain peace and order, the guild leaders had no choice but to banish him.
He might become more brooding and distrustful. Banishment is a harsh experience, and Natsu, who was always so close to his Fairy Tail family, would feel betrayed. This could lead to him suppressing his emotions and becoming more solitary as he tries to figure out how to clear his name.
Another fanfiction concept could be that Erza somehow ends up in the Naruto universe. She might join Naruto's team for a mission. Erza's strong sense of justice and her powerful magic would be really interesting to see in the context of Naruto's world. For example, she could use her armor magic to help Naruto and his friends in a battle against a powerful enemy.