Well, they might be really embarrassed at first. Naruto could turn bright red and stutter, while Hinata might faint from the shock. Then they would probably avoid each other for a while, until their friends notice the strange behavior and try to get them to talk it out.
In the fanfiction, it could be that Hinata is already proficient in kenjutsu. She then teaches Naruto some of the basics. As Naruto learns, they start to have a better understanding of each other's fighting styles. This could lead to them working together more effectively in future battles and also in their relationship development.
In a fanfiction, they could be involved in a race. Naruto's speed, Sasuke's sharingan - enhanced perception, and Hinata's byakugan - aided navigation could all play a part. Maybe they start off competing against each other but then realize that there's an outside threat during the race. So they put aside their differences and work together to overcome the threat, forging a stronger bond in the process.
The fanfiction could show how their relationship deepens during the pregnancy. They could have more quiet, intimate moments together, like sitting on the porch at sunset and talking about their hopes for their child. Hinata could share her dreams of their child growing up strong and kind, like Naruto.
Well, it could be that they have a sleepover at Hinata's place. They might cook a simple meal together like ramen. And then, while sitting around, Naruto could accidentally fall asleep first. Hinata might then take a moment to watch him sleep peacefully, blushing a bit as she realizes how much she cares for him. Later, she might cover him with a blanket and quietly go to sleep herself.
They might visit the local market. Naruto would be excited about all the different foods and items, and Hinata would be happy to follow him around. They could buy some cute souvenirs or some new ninja tools for Naruto. Then they could sit at a small cafe and enjoy some tea while talking about their friends and family.
In a Naruto and Hinata date fanfiction, they could start their day by visiting the memorial stone. Naruto would tell Hinata about his friends who sacrificed themselves. Then they would take a walk in the forest, holding hands and enjoying the peaceful nature around them. Hinata might shyly give Naruto a flower she picked along the way.
There could be a scenario where Kushina comes back to life somehow in the fanfiction. She might then play matchmaker between Naruto and Hinata, using her knowledge of Naruto to help Hinata understand him better. For example, she could share stories of Naruto's childhood that would make Hinata feel closer to him.
It could also result in a change in the way the village views their relationship. Since Naruto is a hero, his saving of Hinata would be a big deal. This could lead to the village elders or the people in general being more accepting of a possible romantic relationship between them. For example, they might start to see Hinata as a more important figure in Naruto's life and give her more respect.
Well, in a 'naruto absorbs hinata fanfiction', Naruto could absorb Hinata's gentle and kind-hearted nature along with her skills. This might change his personality a bit, making him more empathetic. And perhaps he could use Hinata's family techniques in a new and creative way, like combining the Gentle Fist with his Rasengan.
Perhaps in the fanfiction, there's a tournament or a competition. Naruto would be eager to prove himself, Hinata would be quietly determined, and Renamon could show off her combat skills. Their interactions during the event could lead to new friendships and rivalries. They might also learn new techniques from each other during the process.