Well, with Naruto being adopted by the Fem Kyuubi, there would likely be a significant change in his power development. Instead of relying solely on his own chakra and the Nine - Tails' power in the traditional sense, he could have a more harmonious relationship with the Fem Kyuubi's power right from the start. This could lead to him developing new jutsu at a faster pace. Also, the story could explore how Naruto deals with the stigma that might come with being associated with the Kyuubi in a more direct way, since he is now so closely related to the Fem Kyuubi.
It could be a very interesting story. Maybe the Fem Kyuubi would teach Naruto some unique skills that are different from what he learned in the original series. She could also offer him a different kind of emotional support, like a motherly figure.
His relationship with Sasuke would be different. Sasuke might view Naruto's connection with the Fem Kyuubi as a new source of power and be more wary or even jealous. But Naruto could use his new situation to try and bring Sasuke back to the right path earlier.
Well, in this fanfiction, Naruto might have a very different relationship with the fem Kyuubi. He could be more protective of her. Maybe he'd have to teach her about the human world and its ways.
If Naruto was adopted by Kyuubi in fanfiction, it could lead to a completely different Naruto. He might be more confident earlier on. Since Kyuubi is a very powerful being, Naruto could be trained in unique ways. For example, he could learn how to harness Kyuubi's power more effectively without the need for the traditional methods of suppressing and drawing on the fox's chakra. This would change his relationships with his peers too. He might be seen as an oddity, but also as someone with great potential.
Naruto and the Fem Kyuubi could team up due to a twist of fate. Maybe an outside force tries to take advantage of the Kyuubi again, and Naruto realizes that the only way to protect both himself and the Kyuubi is to work together. They would form a pact where Naruto would have access to more of the Fem Kyuubi's power in exchange for helping her get revenge. They would start small, by causing trouble for the lower - level ninja who have always taunted Naruto. As they gain confidence, they would move on to bigger targets, like the village council who have made decisions that have affected both of them negatively.
She might like the ones that focus on character development. For example, fanfictions that explore Naruto's growth in ways not shown in the original, or how other characters around him change over time. These can give her a deeper understanding of the characters she already loves from the Naruto series.
Maybe Kyuubi likes fem Naruto fanfiction because it offers a different perspective on the character. A female Naruto could have different emotional responses and interactions compared to the male version, which might be more interesting to Kyuubi.
In this kind of fanfiction, Naruto could be an ordinary ninja with extraordinary determination. He might develop his skills through sheer hard work and unique training methods not related to the Kyuubi's power. For example, he could focus more on his family's secret jutsu if there was any, or he might be trained by a hermit ninja who has a different approach to combat. This would change his journey entirely as he would not have to face the prejudice that comes with being a Jinchuuriki.
Well, in such a fanfiction, Naruto might grow up with a very different set of values. Since Kyuubi is a powerful and somewhat wild entity, Naruto could be more aggressive in his approach to things. He might have a better understanding of chakra from a very young age as Kyuubi is a huge source of it. Also, his relationship with the village might be more strained as they would be very wary of someone raised by the Kyuubi.
In this kind of fanfiction, Naruto might grow up with a very different personality. Since Kyuubi is a powerful and somewhat wild entity, Naruto could be more fearless and have a deeper understanding of chakra from an early age. He might also have a more aggressive fighting style, influenced by Kyuubi's nature.
The Fem Kyuubi being banished by Minato could lead to a rift between the village and the Kyuubi. In the story, this could mean that the village is more vulnerable to attacks from other threats, as the Kyuubi was a deterrent. For Naruto, it could mean that he has to face the consequences of his father's actions. He may be shunned even more by the village because of his connection to the banished Fem Kyuubi. Also, the Fem Kyuubi herself may become bitter and vengeful, which could pose a major threat to the village and Naruto in the long run.