There could be original characters as well. In fanfiction, authors often create new characters to add to the story. For example, a new ninja from a hidden village who has a special doujutsu that somehow connects with the Kyuubi's power. This character could become an ally or an enemy to Naruto. They could bring in new plot elements, such as a new form of chakra that is only accessible through the combination of their doujutsu and the Kyuubi's power, which would make for a very exciting and unique story.
Naruto is usually a main character as he has a connection with the Kyuubi. Since he already has the Kyuubi sealed within him, it's logical that he would be the one to potentially unlock or develop the Kyuubi doujutsu. Sasuke might also be involved. His rivalry with Naruto could lead to interesting interactions in relation to the doujutsu, either trying to obtain it for himself or learning to counter it.
One interesting concept could be the power dynamics between Naruto and the Kyuubi in relation to doujutsu. Maybe Naruto gains a unique doujutsu ability because of his connection with the Kyuubi. For example, he could have a doujutsu that allows him to better control the Kyuubi's chakra or even see the memories of the Kyuubi's past hosts.
Naruto himself is often involved. His strong will and determination could make him either a target of hypnosis or someone who has to resist it. Sasuke is also a likely candidate, given his powerful doujutsu, the Sharingan. Hypnosis could potentially be used to manipulate his actions or unlock hidden aspects of his Sharingan powers.
Obviously, Naruto is the main character as he is the one releasing the Kyuubi. Sasuke could also be involved, perhaps as an ally or an antagonist depending on the plot of the fanfiction. Sakura might be there too, trying to support Naruto in controlling the Kyuubi's power or dealing with the aftermath.
Kakashi could be involved as well. As Naruto's mentor, he would likely be concerned about Naruto's well - being and how he is handling the fusion. He might try to guide Naruto in controlling the power and also protect him from those who would seek to take advantage of his new - found strength.
Obviously, Naruto is the central character as it's about the Kyuubi being released from him. Sasuke also often plays a crucial role. He might be concerned about Naruto's new state, or he could be one of the characters trying to either help or stop Naruto depending on the plot.
In 'naruto kyuubi doujutsu fanfiction', a cool concept is the potential for new jutsu creation. Since the Kyuubi is a powerful entity, the doujutsu could enable Naruto (assuming he has it) to combine his regular ninjutsu with the Kyuubi's power in novel ways. Maybe he could create a fire - based jutsu that has the added effect of draining the opponent's chakra, as the Kyuubi is known for its voracious chakra appetite. Also, the doujutsu might have a special mode for communication with other tailed beasts.
It could be a doujutsu that has the power of elemental control. For example, it could allow Naruto to manipulate fire or water chakra more effectively just by looking at it. This would be a great addition to his existing skills as he already has a large amount of chakra.
One possible power is the ability to see through illusions more easily. Since the Kyuubi is a powerful entity, a doujutsu from it could give Naruto an edge against genjutsu users. It could break through complex illusions that would otherwise trap 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.