It could be Dumbledore in a lot of fanfictions. Dumbledore often plays a key role in these stories and his reasons for summoning Harry could vary. Maybe he wants Harry to prove himself in a different way, or he has some premonition about the tournament that only Harry can help with.
One possible scenario in this fanfiction could be that Harry and Fleur form an unexpected alliance during the Triwizard Tournament tasks. They might discover they have complementary skills, like Harry's courage and Fleur's elegance and magic related to water (since she's from Beauxbatons). This alliance could lead to them facing the challenges in a new and interesting way, perhaps with Fleur using her Veela charm in a creative manner to distract the obstacles while Harry uses his Gryffindor bravery to take on the more physical parts of the tasks.
One great fanfiction could be where Harry and Luna team up in a unique way during the Triwizard Tournament tasks. Maybe Luna uses her off - beat magical knowledge to help Harry solve the puzzles in the maze. For example, she might recognize some magical creatures that Harry is unfamiliar with and guide him through.
One possible fanfiction could be about Harry and Hermione teaming up secretly during the Triwizard Tournament tasks. They might use their combined knowledge and skills to outwit the other competitors. For example, in the maze task, they could have a special code to communicate and find their way to the Triwizard Cup faster than anyone else.
It could also be due to personal reasons related to his growth and self - discovery. The events of the Triwizard Tournament might make him realize that he needs to find his own path outside of Hogwarts for a while. He might feel that the school can't offer him the answers or the experiences he needs at that moment to become stronger and more independent.
In some fanfictions, when Harry is summoned for the Triwizard, he might face new and unexpected challenges. For example, there could be a twist in the tasks that are not in the original story. Maybe the magical creatures in the tasks are more dangerous or have different abilities.
In some fanfictions, the author might explore the idea that the person who dragged Harry into the Triwizard Tournament has a personal vendetta against him. Maybe it's a relative of a Death Eater who wants to see Harry fail publicly or even die during the tournament. Harry then has to not only survive the tasks but also figure out who is behind this plot against him.
Maybe in fanfiction, Harry hates the Triwizard Tournament because it brings too much danger and unwanted attention. He has to face powerful opponents and deal with complex rules that he may not be fully prepared for.
One common theme is the idea of unexpected relationships. Given that Harry and Fleur don't interact much in the original series during the Triwizard Tournament, fanfictions often explore the possibility of a closer bond between them, whether it be friendship or something more romantic.
One possible fanfiction could be about Harry getting amnesia during the Triwizard Tournament and Luna being the one to help him remember. Maybe she uses her unique perspective and knowledge of magical creatures and odd things to jog his memory. For example, she might take him to see the Thestrals, which are associated with death and memory in the wizarding world.