Well, in such a fanfiction, it might start with Naruto being in a situation where he becomes Madara's pet. Maybe at first, Naruto is defiant but as time passes, he could start to understand Madara's motives in some strange way. Madara, on the other hand, might initially see Naruto as just a possession but gradually develop a sense of attachment. It could be a really strange and complex relationship that unfolds as the story progresses.
In some fanfictions, it could be through a strange and powerful jutsu transfer. Maybe Madara, on the verge of defeat, decides to transfer his Rinnegan power to Naruto for some unforeseen reason, like seeing a new path for the ninja world in Naruto.
In this kind of fanfic, the author may describe Naruto's resemblance to Madara in terms of their auras. Naruto could have an aura that is as intimidating as Madara's. For example, when he enters a room, people might feel the same kind of pressure as they would when Madara was around. And perhaps Naruto starts to have some facial expressions that are similar to Madara's, like a certain smirk or a serious frown.
In a Naruto fanfiction where he has Madara's attitude, he could become more power - hungry. Madara was always seeking power to reshape the world according to his ideals. Naruto might start to view the tailed beasts not as friends but as tools for greater power. He could try to gather more chakra and perhaps even attempt to unlock new forms of power that are more in line with Madara's dark and ambitious nature, which would shock his comrades and enemies alike.
Perhaps in this fanfiction, there's a secret prophecy about Naruto being the grandson of Madara and Tobirama. This leads to a lot of political intrigue within the village. Some people want to use Naruto for their own gain, while others are afraid of what his true heritage might mean for the future of the Hidden Leaf.
In a fanfiction where Naruto is Madara's great - grandson, it would be fascinating to explore how his character develops. He might struggle with the darker side of his heritage, considering Madara's actions. However, he could also use his Uzumaki spirit to bring a new perspective to the Uchiha legacy. His relationships with Sasuke would be especially complex, as they would be related in a much more direct way than in the original story. Naruto could also potentially unlock new forms or powers related to his Uchiha bloodline, which would add a whole new layer to his battles and adventures.
One great 'Naruto and Madara Uchiha' fanfiction is 'The Redemption of Madara'. It offers a unique take on how Madara could have been redeemed in the Naruto universe. It has a great plot that keeps you hooked from start to finish.
On a broader scale, the ninja world would enter a new era. The threat that Madara posed would be eliminated, and Naruto would likely have a major role in shaping the new world order. He might focus on peace - building initiatives and forging stronger bonds between the different ninja villages.
Fanfiction about Madara's memories can also focus on his relationship with Hashirama. We often see in these stories how their friendship was initially pure but then got torn apart by the political situation. This can give us new perspectives on the whole ninja world's history and how the two most powerful shinobi of their time had different views on peace.
In some fanfictions, Naruto could be depicted as Madara's reincarnation. Fanfiction allows for a lot of creative liberties, so authors might come up with such an interesting concept to explore new storylines and character dynamics. However, in the original Naruto series, there is no such indication that Naruto is Madara's reincarnation.