Perhaps the female furry is a messenger from a different dimension. Naruto is the only one who can understand her language at first. They embark on a journey to find a way to send her back to her own dimension. Along the way, they form a deep bond. The female furry teaches Naruto some unique skills from her world, and Naruto shows her the values of friendship and perseverance in the Naruto universe. As they get closer to finding a solution, they have to face powerful enemies who want to use the gateway between the dimensions for their own evil purposes.
A possible plot is that the female furry has a special connection to a powerful chakra - based entity. Naruto is intrigued by this and wants to learn more. As they interact, they face challenges from other ninja clans who are jealous or afraid of this new connection. Their relationship develops as they fight together against these threats and also learn about each other's cultures and backgrounds.