His relationships could change quite a bit. His friends might be a bit intimidated at first. For example, Sakura might be worried about this new, unknown power. But over time, they would probably come to accept it. His enemies, on the other hand, would be more cautious around him.
Well, in a fanfiction where Naruto has Sans eye, it could start with Naruto finding himself in a dimension where he's given this strange power. The Sans eye might give him a new perspective on the concept of chakra, perhaps seeing it in a different form or being able to manipulate it in ways he couldn't before. He could use this new power to better understand his enemies and their motives, and it could also create some interesting interactions with his friends who would be both amazed and a bit wary of this new power.
One drawback could be that it might disrupt the balance of powers in the Naruto world. Naruto was already a powerful ninja, and adding Sans' powers could make him overpowered compared to others, which might make the story less interesting as there would be less of a challenge for him.
Well, in some fanfictions, he might obtain it through a strange encounter. Maybe he stumbles upon an ancient relic during a mission that contains the power of the broken eye dojutsu and it somehow bonds with him.
I like 'Naruto and Sans: A Cross - Over Adventure'. In this fanfiction, Sans uses his shortcuts to help Naruto move around quickly during battles. It also delves into how their personalities, Naruto's determination and Sans' laid - back but intelligent nature, complement each other in the story.
First, get to know the characters well. Naruto is from a world of ninjas with his own set of jutsus and a strong will to protect his friends. Sans is from Undertale, laid - back but with powerful bone - related attacks. Then, think of a scenario that could bring them together, like a rift in dimensions. Just start writing and let the ideas flow.
It might have the ability to see through illusions that normal eyes can't. Since it's a dojutsu, even if it's broken, it could still have some enhanced visual powers. For example, it could detect the tiniest movements of an enemy, giving Naruto an edge in combat.
The third eye might have the power of long - distance vision. Naruto could use it to spy on enemy camps or look for missing comrades from afar. This would be a useful addition to his skills, especially when planning strategies or rescuing hostages. He could also use it to keep an eye on the Akatsuki's movements across different regions without having to be physically close.
If Naruto had a third eye in fanfiction, it could greatly enhance his perception abilities. He might be able to detect hidden enemies or traps more easily. For example, in battles, he could see chakra movements from all directions without having to rely so much on his regular senses. This could make him even more formidable in combat and change the dynamics of his fights against powerful foes like Sasuke or Pain.
It could be due to a battle injury. Maybe he got into a really tough fight with a powerful enemy, and in the process, lost an eye. For instance, a fight against a rogue Akatsuki member who has a very dangerous eye - related jutsu.