Mikoto could be developed as a more powerful figure. Since she has the Sharingan, she could be shown exploring and mastering abilities that were not fully explored in the original series. For example, she might discover a new type of genjutsu unique to her Sharingan that she then uses to protect the Uchiha clan.
Mikoto could influence Naruto's understanding of the Sharingan by sharing her own experiences with it. As an Uchiha, she has first - hand knowledge of the power and the curse that comes with it. She could tell Naruto about the different levels of the Sharingan and how to unlock them. This would give Naruto a new perspective on the power and how to use it effectively.
One way this could occur in the fanfiction is if there was some sort of genetic manipulation. Maybe a rogue ninja or a mad scientist found a way to combine Uchiha genes with Naruto's. Mikoto, being an Uchiha, had the Sharingan, and through this unethical genetic process, Naruto ended up with the Sharingan. This would also open up a whole new set of abilities and challenges for Naruto as he has to learn to control this new power which is very different from his normal chakra - based powers.
Another plot could revolve around a time - travel scenario. Naruto gets sent back in time and meets a young Mikoto. They form an unlikely friendship. Mikoto, seeing Naruto's strange abilities and determination, decides to help him understand the Sharingan better. In the process, Naruto ends up changing the future of the Uchiha clan in some way, preventing the tragedy that was to befall them.
He would gain new visual abilities. Naruto could now use the Sharingan's powers like predicting movements, copying jutsus more easily. But it might also come with some drawbacks. For example, the Sharingan consumes a lot of chakra, so Naruto would have to manage his energy better.
Perhaps a story where Mikoto's Sharingan has a prophecy locked within it. Naruto, with his unwavering belief in changing destinies, helps Mikoto unlock this prophecy. It could be about a future that is both a threat and an opportunity for the ninja villages. Together, they have to figure out how to either prevent or embrace this future.
Well, it could be that Mikoto is trapped in a dangerous situation like a collapsing building or a genjutsu. Naruto, with his strong will and powerful chakra, breaks the genjutsu or rescues her from the rubble. He might sense her distress using his Sage Mode or his connection to the Nine - Tails' chakra and rush to her aid.
In fanfiction, Naruto could get the Sharingan through a blood - related connection that is revealed later. For example, it could be discovered that he has some distant Uchiha ancestry that gets activated somehow. Maybe a powerful enemy's attack awakens this dormant Uchiha blood in him, and as a result, he develops the Sharingan. It could also be that a powerful sage or a new character uses their own unique powers to bestow the Sharingan upon Naruto for a specific purpose.
If Naruto had the Sharingan in fanfiction, it would likely lead to some interesting power - up scenarios. He could combine the power of the Sharingan with his own massive chakra reserves. This might make him an even more formidable opponent. His training would also take a new turn as he'd have to learn to control and master the Sharingan's abilities, like the different levels of the Sharingan and their unique powers.
Naruto might adapt by first trying to understand the basic functions of the Sharingan. He could start with the simple ability to see chakra flow more clearly. Since he has always been perceptive about people's emotions, he could use the Sharingan to read the emotions of his enemies through their chakra, which would help him in battles.