Maybe there are other Grimm that see the pet Grimm as an outcast for being with a human. These Grimm could come after the pet and Jaune, making them the antagonists. They would try to either kill the pet and bring it back to the Grimm world or kill both Jaune and his pet to keep their world 'pure'.
Well, perhaps the plot could involve Jaune trying to train the pet Grimm. He might face challenges from other characters who are against having a Grimm as a pet due to their inherently dangerous nature.
Maybe there are other dragon hunters in the story. These hunters see Natsu's pet dragon as a valuable trophy. They don't care about the bond between Natsu and the dragon. They just want to prove their skills by taking down such a powerful creature. So they keep chasing Natsu and his dragon throughout the fanfiction.
Maybe a powerful wizard or sorceress who has a grudge against Jaune Arc or the fox's kind. This antagonist could try to use magic to break up their marriage or cause trouble between them. For example, they could cast spells to make the fox lose her memory of Jaune Arc or create illusions to make Jaune Arc distrust the fox.
It could be an original character created specifically for the fanfiction. Maybe a mysterious woman Jaune met during one of his adventures who he had a brief relationship with.
One idea could be that the female Grimm is an outcast among her kind. Jaune, with his sense of justice, tries to understand her instead of immediately fighting. They form an unlikely alliance and learn from each other, with Jaune teaching her about the value of life and she showing him the secrets of the Grimm world in return.
The pet could be a small dragon. It would be really cool if Izuku had a dragon as a pet. Dragons are often associated with power and mystery in many fictional universes.
One possible plot could be that Jaune discovers his pet wolf has special powers. For example, the wolf can communicate telepathically with Jaune. They go on adventures together, using the wolf's powers to solve mysteries or defeat enemies in their world.
In a fanfic like this, there could be a lot of conflict. The Grimm's presence could be seen as a threat by the Hidden Villages. Naruto would then have to convince everyone that his pet Grimm is not a danger. Also, the Grimm might have special abilities that Naruto could use in battles or to solve problems in the village. For example, if the Grimm can fly, Naruto could use it to quickly reach far - off places or spy on enemies. And Naruto could also teach the Grimm some of his ninja values, like loyalty and perseverance.
It could be a new dark wizard who wants to use Harry's daughter to get revenge on Harry. This wizard might be jealous of Harry's fame and power and think that by harming his daughter, he can destroy Harry's happiness.
The old shinobi council from his former village could be antagonists. They might still see Naruto as a threat even in exile and try to harm his kids to prevent them from becoming powerful. Or perhaps some new villains who want to use Naruto's kids to get to him, knowing his strong bond with them.