Zabuza could be portrayed as more of a mentor figure. Instead of just being a ruthless assassin, he could be shown guiding Naruto in some aspects of combat or strategy. Maybe he survived his encounter with Kakashi and had a change of heart, and now he imparts his knowledge to Naruto who is now a sensei himself.
Zabuza could be quite cold to Naruto at the beginning. He's not exactly the warm - and - fuzzy type. But when Naruto shows his skills and tells his story of being banished unjustly, Zabuza might empathize on some level. He might not show it openly, but he could start to protect Naruto in his own way, perhaps because he sees a bit of his younger self in Naruto who was also wronged by the ninja system.
In such a fanfiction, Naruto might teach Tsume new ninjutsu skills. For example, he could share his unique Rasengan technique, explaining the chakra control required step by step.
The social status in the village could also be a problem. Naruto is a hero to the village, but he also has his share of enemies. Tsume, on the other hand, has her own standing in the village. Their relationship could make them targets for those who oppose Naruto or who don't like the idea of an Inuzuka getting involved with an Uzumaki. Also, they would need to balance their duties as shinobi with their relationship, which can be really tough.
He could learn Zabuza's signature water - style jutsu, like the Hidden Mist Technique. This would give Naruto an advantage in terms of creating diversions and hiding his movements during battles.
In this fanfiction, Naruto might save Tsume from a powerful enemy. Maybe he uses his Rasengan to defeat the foe who has Tsume cornered. His quick thinking and combat skills could be the key to her rescue.
It's likely a mentorship relationship. Naruto, as Tsume's master, would be in a position of authority and guidance. He'd be responsible for Tsume's growth as a ninja.
On a more practical level, Naruto's skills might be misused. Instead of using his power to protect Konoha and the people he cares about, he's using it for Zabuza's self - centered motives. This could also make him a target for other ninja who oppose Zabuza. So not only is he in danger from the people he used to call friends, but also from new enemies. And if he ever tries to break free from Zabuza, he might face severe retaliation from Zabuza himself, which could be life - threatening.
A minor character like a blacksmith's apprentice could find Zabuza's sword. Instead of using it for fighting, they study it closely. They discover a unique metal alloy in the sword that they use to create new and improved weapons for their village. This not only changes their own fate as they become a renowned blacksmith, but also the fate of the village as they now have better weapons to defend themselves.