Yes, there are quite a few. Some might explore what would happen if Arturia was a student at Hogwarts. She could bring her unique magical abilities and chivalrous code into the wizarding world. For example, she might interact with Harry Potter and his friends in a way that changes the course of some of their adventures. There are also fanfictions that could involve Arturia facing off against Voldemort, which would be an epic battle of two very different forms of magic.
A good way is to establish a common ground. For instance, if both universes have a form of magic, find a way to make those magics interact. Maybe Arturia's magic can be seen as an ancient form that has been forgotten in the Harry Potter world. Another way is through character relationships. Harry could look up to Arturia as a mentor figure, learning from her noble and chivalrous ways.
One interesting concept could be a crossover where Arturia Pendragon ends up at Hogwarts. Maybe she uses her swordsmanship skills to teach the students a new form of magical combat. Another idea is that she could be on a quest related to the Deathly Hallows, bringing her own Arthurian magic into the wizarding world of Harry Potter.
One common plot element is the crossover of magic systems. Arturia's magic from the Arthurian legend and the magic in Harry Potter often interact. For example, her ability to use magic without a wand might be a shock to the Hogwarts students. Another is the character relationships. Arturia could become friends or foes with the main characters in Harry Potter. For instance, she might be a rival to Hermione in terms of magical knowledge.
The clash of two different magical universes. Harry Potter has its own set of magic rules, spells, and creatures, while Arturia comes from a completely different magical world in the Fate series. When combined, it creates a unique and exciting setting.
There's also 'Fate and Hogwarts'. This fanfic imagines Arturia as a transfer student to Hogwarts. It's really cool as it shows how she adapts to the new magical environment. The author does a great job of blending the two different magical systems and making it seem believable. There are some really intense duels and a growing friendship between Arturia and Harry that keeps the story engaging.
One possible aspect of Lancelot x Arturia fanfiction could be the exploration of their complex relationship. Lancelot's loyalty and his inner conflict due to his feelings for Arturia can be a central theme. Their relationship is often portrayed with a sense of tragic beauty, as they are both bound by their own fates and the code of chivalry.
The appeal lies in the forbidden love aspect. Their relationship goes against the norms of the Arthurian court and the chivalric code in some ways. It adds a sense of drama and excitement.
Another aspect to consider in this fanfiction is the cultural clash. The feudal - like society in the Naruto world and Arturia's own Arthurian era background. Arturia might find the concept of ninja villages and the way they are structured quite strange. At the same time, Naruto and his friends could be fascinated by Arturia's tales of Camelot and the Round Table.
A great idea for this fanfiction would be to explore how Arturia adapts to the ninja world. She would have to learn about chakra and ninjutsu. Maybe she could combine her own magic with chakra to create unique attacks. For example, infusing Excalibur with chakra to make it even more powerful. This would also make for some really cool fight scenes in the story.