It could be to explore how a wizard from the Harry Potter world would interact with the ninja - based Naruto world. To see how his magic would fare against ninjutsu, and what kind of chaos or harmony it would bring. So, that's a possible reason for him to be summoned in the fanfiction.
Maybe for the sake of an interesting crossover. Writers often bring different characters from various universes together to create unique and exciting stories.
It's a wild concept. Naruto is from a world where physical combat and chakra control are key, while Harry Potter's world is centered around magic. If summoned, Naruto could be seen as an otherworldly being. His presence could create chaos as the wizarding world tries to figure out how to deal with him. He might start challenging the dark wizards using his own brand of justice.
It could be a young, inexperienced ninja who accidentally summons Naruto while trying to perform a different summoning jutsu. Maybe they were aiming for a small animal to help them with a simple task, but due to their lack of skill, they end up with Naruto. Another possibility is an enemy of Konoha who wants to use Naruto as a bargaining chip against the village. They think that by having Naruto in their hands, they can force Konoha to meet their demands.
It could change the whole dynamic of battles. The animatronics might have unique abilities that could give Naruto an edge.
It could be that the Order has a plan that only Harry can be a part of. His unique experiences and skills, like his ability to resist the Imperius Curse and his connection to Voldemort, are valuable. So they summon him to put these to use in their fight against the Dark side.
When Harry is summoned by Naruto fanfiction, it's likely that he would be a fish out of water. He would encounter characters like Naruto, Sasuke, and Sakura. His magic skills could be seen as a new form of power in that world. He might get involved in the battles between the ninja villages, using his own unique abilities to help or cause chaos, depending on how the story is written.
Well, he might use his ninja skills to become a hero in that world. He could teach the locals about chakra and how to fight like a shinobi. Maybe he'd make new friends and form a team to face the challenges there.
Their interaction could be initially rocky. Naruto is loud and brash, while Jeanne is more reserved and devout. But as they get to know each other, they could learn from one another. Naruto could show Jeanne some of his ninja tricks, and Jeanne could teach Naruto about her cause and the importance of her mission.
He would probably use his leadership skills. Naruto has grown into a great leader as Hokage. In the past, he could quickly assess situations and lead others, whether it's in a battle or in village - building activities.
He might become more strategic. As a ninja, Naruto was often head - on in his approach, but as an Archer, he'd have to think more about distance and positioning. His brashness might tone down a bit as he realizes the importance of stealth and surprise when using a bow. For example, he'd need to find good hiding spots before taking a shot.
Harry might cry in fanfiction due to the overwhelming pressure he faces. He has the weight of the wizarding world on his shoulders. Saving everyone from Voldemort is no easy task, and the stress could make him break down in tears.