One possible plot could be that Naruto, with his godlike powers, stumbles upon Artemis in the forest. Maybe he helps her protect the forest from some dark force. His powers, like his shadow clones and Rasengan, could be adapted in a unique way to fight alongside Artemis's archery skills.
Well, perhaps in the fanfiction, Naruto's godlike status makes him a target. Artemis, being a goddess, decides to help him. Their relationship could start as a begrudging alliance but then develop into a deep friendship. They might face challenges like other gods being jealous of their new - found bond and trying to break it up. Naruto could teach Artemis about the ninja way, and she could introduce him to the ways of the Greek gods.
In this fanfiction, it could be that Naruto has been sent to the world of Artemis on a mission. His godlike abilities are needed to stop a great evil that is threatening both the ninja world and Artemis's realm. As they journey together, they learn about each other's cultures and powers. Naruto's ability to sense chakra could be used to detect hidden threats in Artemis's forest, while Artemis's hunting skills could help Naruto track down enemies in a new and unfamiliar territory.