He might isolate himself. Naruto has always been a social person, but the heartbreak could be so intense that he just wants to be alone. He might go to his favorite training spot and just train by himself for days, trying to forget the pain through physical exertion.
Naruto could also try to find distractions. He might take on more dangerous missions or get involved in village politics more than he usually would. By keeping himself busy, he hopes to not think about Hinata and the heartbreak she has caused him. In some fanfictions, he even leaves the village for a while to explore the world and get away from the memories associated with her.
Sometimes, he might seek support from his friends. Although it's a heartbreak caused by Hinata, Naruto has a strong group of friends like Shikamaru or Sakura. They might offer him advice or just be there to listen. But it could be a struggle for Naruto to open up, as he is used to being the strong one. However, eventually, with their help, he might start to heal slowly.
He might isolate himself at first. Natsu could withdraw from his friends and normal activities, needing time alone to process his pain. This is a common way for people, or in this case, characters, to deal with heartbreak.
Naruto might throw himself into his ninja training. He's always been dedicated to getting stronger, and heartbreak could fuel that drive even more. For example, he could spend countless hours perfecting new jutsu or sparring with his friends. Another way he could cope is by relying on his friends. Sakura and Kakashi, for instance, could be there to support him, listen to him vent, and offer advice. He might also find solace in eating ramen at Ichiraku. The familiar taste and the warm atmosphere of the ramen shop could give him some comfort.
Another character could be Kakashi. Maybe he has to make a tough decision that goes against Fem Naruto's wishes. For example, not allowing her to go on a dangerous mission she really wants to. This could make Fem Naruto feel betrayed and heartbroken, as Kakashi is a respected figure in her life.
Hinata supports Naruto by being his emotional anchor. When facing the Juubi, Naruto can get caught up in the chaos and danger, but Hinata is there to remind him of his humanity and the things he's fighting for. For example, with a simple look or a kind word, she can calm him down in the heat of battle.
Maybe Naruto discovers that the village he has been trying so hard to protect has been using him all along. He might find out some dark secrets about the Hidden Leaf, like they were involved in something immoral and were just using his power, which would shatter his idealistic view of the village and leave him heartbroken.
There's a fanfic titled 'Hinata's Comfort for Naruto'. In it, Naruto is heartbroken after a major loss in the village. Hinata, who has long admired him from afar, steps in. She first helps him by taking care of his daily needs like cleaning his messy apartment and doing his laundry. This simple act of kindness makes Naruto realize that someone truly cares. Then Hinata shares her own experiences of feeling alone and how she overcame it, which gives Naruto the strength to start anew.
Naruto would likely stay positive and try to find a way out. He'd probably make some jokes to lighten the mood for Hinata.
One possible reason could be misunderstandings. Maybe Hinata says or does something that Naruto misinterprets in the fanfiction. For example, she might seem to reject his feelings in a really harsh way that breaks his heart.
Naruto also finds solace in his dreams of becoming Hokage. He believes that if he becomes the most powerful and respected person in the village, people will finally accept him. He uses this goal as a driving force to keep going despite the abandonment. He trains hard and tries to improve himself constantly.
Often, it develops from Hinata's long - standing admiration for Naruto. In the context of Naruto being an emperor - like figure, Hinata's respect for him grows even more. Naruto, in turn, begins to see Hinata in a new light, realizing her loyalty and strength. This mutual understanding and respect deepen their bond.