The story could also explore how Naruto's relationship with other characters in the Naruto universe would be affected. His friends like Sakura and Kakashi might be initially suspicious of Sasori's influence on Naruto. But as Naruto shows that he still holds onto his core values, they might come to accept this new situation. And Naruto's enemies would likely be more cautious, seeing that he has new abilities and a different kind of mentorship under Sasori.
His fighting style would probably incorporate a lot of puppetry. He'd use puppets in combat like Sasori does. Maybe he'd also use some of the unique poisons that Sasori is known for. His style would be less about brute force and more about strategy and misdirection.
Naruto being raised by Sasori would be a huge shift. Sasori is not one to show much emotion or promote the ideals of hope and perseverance like the people in Konoha. Naruto would likely have a different sense of loyalty, perhaps more towards Sasori's goals or ideals which are mainly centered around his own power and the art of puppetry. His growth as a ninja would be more focused on silent and deadly skills rather than being a hero that everyone looks up to. His relationships would be more transactional in nature as he wouldn't have been exposed to the deep emotional bonds that are so prevalent in Konoha.
Naruto could become more stealthy. Since Sasori is a master of puppetry, which often involves covert operations, Naruto might pick up on how to move quietly and be more discreet in his actions. This would be a contrast to his usually brash and straightforward fighting style.
In the fanfiction, they could have a mentor - mentee relationship. Naruto, with his big heart and positive attitude, could be the one to show Sasori a different way of looking at things, like a mentor. Or Sasori could teach Naruto some of his puppet - related skills, acting as a mentor in that aspect.
In a fanfiction, Deidara and Sasori could be sent on a secret mission to infiltrate a hidden village. Deidara uses his clay creations to distract the guards while Sasori sneaks in with his puppets. As they progress, they discover a powerful weapon that the village is developing. They then have to decide whether to destroy it or take it for the Akatsuki. Along the way, they also have to deal with their own internal conflicts and the pressure of the mission.
They could be on a journey to find a rare material for Deidara's art. Sasori, with his knowledge of the ninja world, helps guide them. Along the way, they encounter various strange creatures and ninja clans. They might have to fight off some who are after the same material.
In the 'naruto is like sasori fanfiction', they might share a sense of being outsiders. Naruto was an outcast as a child because of the Nine - Tailed Fox inside him. Sasori was also kind of an outlier in the Sand Village. In the fanfic, their personalities could be molded to show how they both deal with this outsider status, perhaps with Naruto's more positive outlook influencing Sasori in some way.
A possible plot could involve Sasori taking Naruto as an apprentice to make up for his past mistakes. He could see potential in Naruto to use his puppet - making knowledge for good. And Naruto, being the eager learner he is, would soak up all the knowledge, and eventually use it to defend the Hidden Leaf against new threats.