Naruto would likely gain the ability to use all six paths techniques. The Rinnegan allows the user to manipulate gravity, as seen when Madara used it. Naruto could use this to enhance his combat skills, for example, pulling enemies towards him or pushing them away forcefully. He could also use the Preta Path to absorb chakra, which would be a great addition to his already large chakra reserves.
With the Rinnegan, Naruto might gain the power of the Outer Path. This could give him the ability to revive the dead, which would be a huge change in the Naruto universe. He could also use the Animal Path to summon powerful creatures. And his Sage Mode could potentially be enhanced by the Rinnegan, giving him even greater perception and power in battle. The combination of his existing abilities like the Rasengan and the new Rinnegan - based powers would make him an even more formidable opponent.
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.
The Sharingan might also give Naruto the ability to enter people's minds, at least to some extent. In the Naruto universe, the Sharingan has been shown to have some mind - related abilities. Naruto could use this to communicate with his friends in a more direct way, or perhaps even to break through genjutsu more easily. And, if he can enter the minds of his enemies, he could gather valuable information about their plans and weaknesses.
Naruto would gain the ability to copy jutsu. With the Sharingan, he could watch an opponent's movements closely and replicate their techniques. This would be a huge advantage for him in battles.
Naruto could gain the ability to manipulate light and darkness, which are often associated with Keyblades. This would be a huge change from his normal chakra - based abilities. He could also use the Keyblade to fly, giving him an advantage in both mobility and combat. Another new ability might be the power to heal, as some Keyblades have restorative properties.
He could gain the ability to see different timelines clearly. The Rinnegan already gives enhanced perception, and with time travel, Naruto could view the consequences of different actions in different timelines. He might also be able to transfer knowledge from one timeline to another. For example, he could learn a powerful jutsu in the past timeline and bring that knowledge back to his original timeline.
He could develop the ability to use the Six Paths Sage Mode more effectively. Since the Rinnegan is related to the Sage of Six Paths, it would enhance his connection to that power. He might also gain the ability to create chakra chains similar to those of the Uzumaki clan but with an added Rinnegan - powered twist.
He could gain the ability to predict his opponents' moves more accurately. The Sharingan is famous for that. So Naruto would be even better at dodging attacks in combat.
He might gain the ability to see chakra in a more detailed way. Since the Rinnegan is known for its enhanced visual perception of chakra, Naruto could use this to his advantage when dealing with Kurama's chakra. He could also potentially use the Rinnegan's power to enter Kurama's mindscape in a new way, maybe with more control and understanding. Another possible ability is to transfer Kurama's chakra to others in a more efficient and controlled manner using the powers of the Rinnegan.
One possibility is through some sort of transplant or transfer. Maybe Madara, before his death, found a way to transfer his Rinnegan to Naruto. It could be a last - ditch effort to pass on his power to someone he saw potential in. Another way could be through some sort of ancient jutsu or curse that links their fates and causes the transfer of the Rinnegan.
He could perform powerful genjutsu with the Sharingan. Naruto, who was not really known for genjutsu before, would now be able to create illusions that are difficult to break. With the Rinnegan, he might be able to use the Six Paths techniques, like the ability to control gravity or absorb chakra attacks.