Well, the Kyuubi itself would probably be changed. Naruto had a deep bond with it. His sacrifice might make the Kyuubi more empathetic towards humans. It could even decide to protect the village in Naruto's memory. On the other hand, the next generation of ninja would grow up without Naruto as their inspiration. They would have to find new heroes to look up to, and the stories of Naruto's deeds would become more like legends, with a bittersweet feeling of what could have been if he had lived.
One consequence could be a huge power boost. Naruto would become extremely strong, which might change the power balance in the fanfiction world. Enemies would be more cautious of him, and allies might rely on him more. Another consequence could be the internal struggle. The Kyuubi has its own will, so Naruto might have to constantly fight to maintain control when it's summoned.
One consequence could be that he becomes extremely powerful. His physical abilities like strength, speed, and endurance are enhanced. He can also use more powerful jutsus with the extra chakra boost from the Kyuubi.
Another consequence could be in his relationships with his friends. Some of his friends might be uncomfortable with the idea of Naruto having the Kyuubi as a slave. They may worry that this new - found power will change Naruto for the worse. However, Naruto could also use this power to better protect his friends and the village. But overall, it's a complex situation that could have far - reaching effects on Naruto's character development and his place in the ninja world.
One possible consequence is that the power balance in the ninja world is completely disrupted. With the Kyuubi's massive chakra and power running free, smaller villages might be constantly in fear of being attacked. Konoha, in particular, would have to find new ways to defend itself without relying on the fact that the Kyuubi is sealed within one of its shinobi.
Well, in fanfiction, the Naruto and Kyuubi fusion could lead to a change in how the ninja world views Naruto. He would be seen as an even greater threat or an even more powerful ally. For example, other villages might be more hesitant to engage in conflict with him. Also, his relationship with his friends could be affected. They might be in awe of his new power but also a bit worried about the Kyuubi's influence on him. And on a physical level, his appearance might change, perhaps taking on some of the Kyuubi's features, like his eyes or his hair color getting a more reddish tint.
In some fanfictions, controlling the Kyuubi chakra might change Naruto's appearance. He could have some physical features related to the Kyuubi, like red - tinted eyes or a more ferocious look when using the chakra. Also, his relationships with others might be affected. Some might be in awe of his new power, while others could be afraid of him.
In fanfiction, the Naruto - Kyuubi pairing can greatly expand the power dynamics. For example, they might be able to defeat stronger enemies together more easily. It can also change the relationships Naruto has with other characters. If he has a closer bond with the Kyuubi, some characters might be more in awe or more fearful of him.
One possible consequence could be that Konoha would enter a period of deep mourning. Naruto is a beloved figure, and his sacrifice would leave a huge void. The villagers might be inspired by his selfless act to strive for a more peaceful and united Konoha. His friends, like Sasuke, might be filled with a new sense of purpose, perhaps to carry on Naruto's ideals in a more aggressive way to ensure his sacrifice wasn't in vain.
He might become much more powerful. With the Rinnegan, he could gain new abilities like the Six Paths powers, which would make him a force to be reckoned with in battles.
One possible consequence could be chaos in the ninja world. With Naruto, a major force for peace, dead and the Kyuubi released, other villages might see an opportunity to gain power or territory. Villages that once relied on Naruto's protection would be vulnerable. Also, the Kyuubi, being a powerful and wild force, could start causing destruction on its own, without Naruto to control it.