Maybe through new jutsu or abilities. The fanfiction could give Naruto some unique power that allows him to communicate or negotiate with the Nine - Tails on a different level. He could use this power to show the Nine - Tails a different perspective, like the potential for harmony between them instead of constant struggle.
Another way could be through some form of emotional connection. Naruto has experienced a lot of loneliness and the Nine - Tails also has its own long - held grudges. By finding a common ground in their emotions, like understanding each other's pain of being used or feared, Naruto could start to tame the Nine - Tails. He could then work towards a more cooperative relationship with the Nine - Tails, which is essential for taming it.