Well, first of all, Naruto would have a proper father figure. Asuma could help Naruto understand the importance of family values. In terms of ninja skills, Asuma could pass on his knowledge of wind - style jutsu more effectively. Naruto would probably be more involved in Asuma's team activities. He might also learn from Asuma how to handle complex situations within the village and among other ninja clans. This adoption would be a huge turning point for Naruto, shaping his future in a very different way compared to the original story.
The plot might involve Naruto being trained by both Kurenai and Asuma to become a more well - rounded ninja. Kurenai could focus on his stealth and genjutsu skills. Naruto, who has mainly focused on his ninjutsu and taijutsu, would benefit greatly from this. As for the relationship with the village, with Kurenai and Asuma as his adoptive parents, Naruto might gain more respect from some of the villagers who previously looked down on him. This could also lead to changes in how he interacts with his peers, like Sakura and Sasuke.
Naruto's character would become more mellow. Kurenai's gentle and nurturing nature would have a calming effect on him. He would be less impulsive. And with Asuma as a role model, Naruto would become more responsible. He would learn the importance of family and loyalty from them.
Naruto's character would likely become more calm and collected. Asuma's influence could tone down Naruto's over - exuberant nature. He might learn to think before he acts more often.
Well, it could be a story full of mentorship. Asuma could teach Naruto his unique jutsu, like the Wind Style. Naruto would also learn about Asuma's values, such as loyalty and perseverance. And perhaps they would bond over a shared love for food. Maybe Naruto would become closer to the Sarutobi family in general.
His relationship with the Leaf Village would become more personal. He'd be part of the Sarutobi clan in a sense. His bond with Shikamaru and Choji would strengthen as they are Asuma's students. Naruto would also have a new father - figure relationship, which would change how he views authority.
In a Naruto saves Asuma fanfiction, Naruto could use his new jutsu skills. Maybe he discovers a way to reverse the damage done to Asuma. It could be related to his Sage Mode powers, which he could use to heal Asuma's wounds.
Well, Naruto might finally get the motherly love he's been longing for. Tsunade could train him more intensively, sharing her medical ninjutsu knowledge too. He'd probably have a more stable home life and grow even stronger under her guidance.
In such a fanfiction, Naruto might gain divine powers. Since Kami is a powerful entity, Naruto could be trained in ways that are far beyond what he learned in the ninja academy. He might also have a different perception of the world and his place in it, seeing things from a more god - like perspective.
If Naruto gets adopted in RWBY fanfiction, it could lead to some interesting team - ups. For example, he could be paired with Ruby. Ruby is all about speed and her scythe - wielding skills, and Naruto's agility and combat skills would complement that. They could create some amazing battle strategies together. Also, Naruto's backstory of being an outcast at first could make him bond with characters in RWBY who have faced similar situations.