The appeal lies in the combination of two very rich and beloved fictional universes. Fans of both 'The Lord of the Rings' and 'Eragon' get to see their favorite elements come together. It's like a dream come true for many, seeing Aragorn interact with Eragon, for instance.
Merlin, being a very wise and sometimes mischievous wizard, would likely be intrigued by Eragon's dragon - related powers. He might start by observing Eragon and Saphira from a distance. Eragon, on the other hand, would be cautious at first, as he doesn't know Merlin's intentions. But once they start talking, Merlin could share some of his knowledge about magic, which would be really valuable for Eragon.
Another possibility is that Percy somehow gets transported to Eragon's world. He has to adapt to the new environment and figure out how his demigod powers work there. Eragon could initially be suspicious of Percy but then they realize they can help each other. Percy could teach Eragon about water magic, which is new in Eragon's world, and Eragon could show Percy how to ride a dragon, which would be an amazing experience for Percy.
The characters would likely be initially cautious. For example, Hermione might be skeptical about the dragon - based magic in Eragon's world. She would want to study it first. Harry, on the other hand, might be more open - minded and eager to learn about Eragon's bond with his dragon. Eragon would probably be curious about the wands and the organized system of magic at Hogwarts.
One idea could be a magical exchange program. Wizards from Hogwarts and Dragon Riders from Alagaësia meet and learn from each other's magical systems. Harry Potter characters could be fascinated by the bond between Eragon and his dragon Saphira, while Eragon might be intrigued by the variety of magic at Hogwarts like Transfiguration and Potions.
One idea could be that Eragon, while on one of his adventures in Alagaësia, accidentally creates a portal that leads him to Hogwarts. There, he meets Harry Potter and they quickly realize they have a lot in common. They could team up to fight against a dark force that somehow threatens both their worlds, like a new type of dark magic that combines the magic of Alagaësia and the dark arts from the wizarding world.
Hermione Granger is quite popular too. Her intelligence and thirst for knowledge can be a great asset in the world of Eragon. She might be the one to figure out how to translate ancient dragon languages or come up with new spells by combining the two magic systems.
Well, it could start with a magical accident. In the Percy Jackson universe, a spell gone wrong sends Percy, Annabeth, and Grover into the land of Alagaësia from Eragon. There, they discover that the demigod powers Percy has are seen as a strange and new form of magic. Eragon is initially suspicious of them but realizes they can help in his fight against Galbatorix. They combine their skills, Percy's water - controlling powers and sword - fighting skills, along with Annabeth's strategic mind and Grover's nature - sensing abilities, with Eragon's dragon - riding and magic - wielding skills to take on the dark forces.
One great 'lotr crossover eragon fanfiction' is 'The Meeting of Worlds'. It combines the magical elements of Eragon's world with the epic scale of Middle - earth in an exciting way. The characters from both universes interact in a believable manner, making for a very engaging read.
One idea could be that Merlin, with his magic from the Arthurian world, meets Eragon in Alagaesia. Maybe Merlin helps Eragon to better understand and control his own magic, as Merlin has centuries of experience. He could teach Eragon about different forms of magic and how to use it more subtly.