Well, it could have a huge impact. Maybe his new power as the Juubi gives him the ability to control time in some way during the time - travel. For example, he might be able to reverse or speed up certain events more easily than he could without that power.
Well, if Naruto becomes the Juubi in a time - travel fanfiction, one possibility is that he could use his new - found power to change the course of history. Maybe he'd prevent some of the great tragedies that happened in the Naruto world. He could also use the Juubi's power to gain a deeper understanding of the chakra system and teach others about it, leading to a new era of ninja development.
One challenge could be controlling his newfound power. The Juubi's power is immense and Naruto might struggle to not accidentally cause destruction while time - traveling. For instance, a simple movement or action might have a much larger impact on the timeline due to his increased power.
Another interesting idea in this type of fanfiction is the character interactions. Naruto could interact with his parents when they were young. He could see how his father was as a young ninja, and how his mother was before she sacrificed herself. This would give him a deeper understanding of his family and his own identity. And with the Juubi's presence, these interactions could take on a whole new level of significance, as he might be able to use the Juubi's power to protect his family in the past, changing the course of his own family's history.
The Juubi eye could potentially be a key factor in the time travel plot. It might possess powers that allow the user to manipulate time or access different timelines. For example, it could open portals to the past or future. This would create interesting scenarios where Naruto has to use the Juubi eye's power to correct past mistakes or prevent future disasters.
His character could become more isolated at first. The power of the Juubi is so great that it might be hard for others to understand him. But as he learns to control it, he could become more confident and wise. He would have to face new moral dilemmas as well, like how much power is too much and when to use it. This would lead to a more complex and mature Naruto.
Naruto would likely be one of the main characters. Since it's a Naruto - centered fanfiction, he'd be the one using the Juubi eye for time travel, probably to save the world or his friends. Sasuke could also be involved. Maybe he initially opposes Naruto's use of the Juubi eye for time travel but later realizes its importance. And there could be villains like Kaguya who might try to stop Naruto from using the Juubi eye's time - travel powers for their own evil purposes.
In this kind of fanfiction, Naruto becoming the Juubi would completely change the Naruto universe. It would mean he has an insane amount of power. He could potentially reshape the world, bring peace in a way no one expected. His relationships with other characters like Sasuke would also be very different. Sasuke might be both in awe and a bit jealous of this new power Naruto has.
In Juubi Naruto time travel fanfiction, plot twists can be really exciting. For instance, Naruto might find out that the Juubi has a different origin in the past than what he thought. This could completely change his perception of the tailed beasts and his role as the Jinchuriki. It could lead to him having to form new alliances or fight new enemies in the past.
If Naruto becomes the Juubi in fanfiction, he would likely gain an incredible amount of power. He might be able to reshape the ninja world. His physical abilities would be off the charts, with strength, speed, and durability far beyond what he had before. His chakra reserves would be limitless, allowing him to perform extremely powerful jutsus without tiring easily. Also, his new form could potentially change the balance of power among the ninja villages, making Konoha the most dominant force. And he could use this power to protect his friends and the entire ninja world from any threat.