In some fanfictions, Naruto having Kyuubi's eyes could signify a deeper connection to the Kyuubi's power. It might mean he can access its chakra more directly or even gain some of the Kyuubi's abilities related to perception, like seeing chakra more clearly.
One interesting concept could be the Kyuubi eyes having unique powers like seeing through illusions that even the Sharingan can't detect. This would give Naruto an edge in battles against powerful foes who rely on deceptive jutsu.
Often, in fanfiction, Naruto with Kyuubi's eyes is shown to have enhanced abilities. Writers may show him using the Kyuubi's eyes to see through illusions more easily. They might also describe his vision as being able to detect the slightest movements or changes in chakra flow. His appearance could also change slightly, with the eyes being a central focus. Maybe his pupils become slitted like a fox's, which adds to his overall otherness. This new look could also attract different reactions from characters in the story, from admiration to fear.
The ability could also affect Naruto's power on an emotional level. Knowing that Kyuubi can see through his eyes might make Naruto feel more confident. He might be more willing to take risks in battles or in exploring new areas. This new - found confidence could translate into him using his existing powers more effectively, like his Rasengan or his ability to summon toads. Also, Kyuubi might be able to spot things that can help Naruto improve his jutsu. For example, if there are certain natural elements or energy sources that Naruto can use to power up his jutsu, Kyuubi could see them through Naruto's eyes and tell Naruto how to utilize them.
Some fanfictions might depict the Kyuubi eyes as having a mind of their own. They could be constantly communicating with Naruto in a silent way, guiding his actions or warning him of danger. It's like they are a separate entity within him that he has to learn to work with.
In some fanfictions, Naruto's mother, Kushina, has a special connection with the Kyuubi. For example, some stories might explore how Kushina's chakra influenced the Kyuubi's behavior. Since she was the Jinchuriki before Naruto, her relationship with the Kyuubi could be a rich source of plot development in fanfiction.
In some stories, the fox eyes might give Naruto a kind of hypnotic or intimidating power. Enemies might be momentarily stunned or less able to fight effectively when they look into his fox eyes. This could be a unique advantage in battles, allowing Naruto to gain the upper hand without having to use as much physical force.
They might have adventures where Kyuubi can use Naruto's eyes to sense hidden threats. For example, in a battle against an unknown enemy, Kyuubi could spot the enemy's hidden traps or ambushes through Naruto's enhanced vision. This would give Naruto an edge in combat as he could be alerted to the danger before it's too late.
Maybe through some kind of special training or a unique ritual. It could be that he discovers a hidden method within the ancient scrolls of his village.
Kyuubi's comfort can make Naruto more confident. Knowing that he has Kyuubi's support, he may take on more difficult missions without hesitation. For instance, if he's facing a powerful enemy, he'll remember Kyuubi's words of encouragement and stand his ground firmly.