Naruto would probably start by trying to be friendly. He might offer them food, like some of the fish he catches. He'd use his energetic and positive attitude to break the ice.
Well, one possible plot could be that Naruto, being his adventurous self, stumbles upon the pack of Houndooms in a hidden forest. He decides to live with them to learn their ways. Maybe he discovers that the Houndooms have a unique form of communication that he tries to master, and this new skill helps him in his future battles or interactions with other ninja.
Naruto, being the friendly and outgoing character he is, would likely start by trying to befriend the Houndoom pack. He might offer them food or play with them. As time goes on, he would respect their hierarchy within the pack and learn their ways of hunting and protecting their territory. He could also share his ninja skills with them, like how to be more agile and quick - thinking in combat situations.
He could also interact with the scientists on Pandora. They might be interested in Naruto's abilities and study him. Naruto could in turn learn about their technology, which is so different from what he has in his own world. He might even help them solve some problems they have on Pandora using his ninja wisdom.
It might be about Naruto living freely in a sense that he can make his own choices regarding his relationships. For example, he could choose his friends and allies more freely without political interference. In this fanfiction, he might not be bound by the traditional shinobi rules and hierarchies, allowing him to interact with different clans and villages on his own terms.
Obviously, the foxes would be the main characters. There could be an old, wise fox that acts as Naruto's mentor among them. It could have a name like Kyo, and it would be the one to teach Naruto the most important lessons.
Gaara would be an obvious choice. Since Gaara is from Suna, he could be Naruto's close friend. They could train together and share their experiences of being jinchuriki. Kankuro and Temari might also become his friends. Kankuro could teach Naruto some of his puppet techniques, and Temari could help Naruto with wind - style jutsu training.
Sasuke could be one of his companions. Even though they've had their differences, they always end up coming together for big challenges. Sasuke's sharingan would be useful on the moon, helping them detect any hidden threats. Another could be Kakashi. His experience and knowledge would be invaluable in a new and strange environment like the moon. He could also teach Naruto and Sasuke new techniques based on the moon's conditions.
In this fanfiction, perhaps Hinata and Naruto are living together and learning more about each other on a deeper level. Hinata could be teaching Naruto some of the traditional Hyuga clan techniques, while Naruto shows Hinata some of his unique jutsu. Their living situation might also involve a lot of visits from their friends like Sakura and Sasuke, creating some really fun and heart - warming group dynamics.
Maybe they start a family and Naruto becomes a great Hokage while Sakura takes care of their home. They face daily challenges together like any normal couple.