A new character could be the main antagonist. Maybe a powerful magic user who is jealous of the ninjas' arrival in the Grand Magic Games. This character could start causing chaos, using dark magic to try and eliminate the ninja competitors because they are seen as a threat to the traditional magic users in the games.
It could be Orochimaru. He might have found a way to enter the Grand Magic Games world and is using his dark jutsu to control some of the magic users. He wants to use the power of the games to become even more powerful and immortal.
It could be a powerful dark wizard who has infiltrated the games under a false identity. This wizard might have a vendetta against Natsu or his guild and wants to disrupt the games and cause chaos.
Maybe the main antagonist is an ancient evil that has been awakened by the chaos of the Grand Magic Games. This entity sees Natsu as a threat to its plans and attacks him, resulting in the loss of his arm. The evil being would then continue to try and disrupt the games and cause more harm to the magical world while Natsu and his friends try to stop it.
Gray Fullbuster could be a great rival. Gray is a powerful ice - make mage. His calm and collected demeanor would contrast with Naruto's more exuberant personality. Gray's precise and powerful magic attacks would pose a serious threat to Naruto, forcing him to come up with new strategies using his ninja skills.
One possible plot could be that Naruto and his friends enter the Grand Magic Games by some strange magic portal. They have to learn new magic skills quickly to compete. Naruto might use his shadow clone jutsu in a creative way combined with magic, like having clones do different magic spells simultaneously.
A great plot could involve Naruto being brought into the world of the Grand Magic Games against his will. At first, he's completely out of his element. But as he starts to understand the rules and the power of magic, he discovers new ways to use his chakra. He might enter a tournament event where his speed and agility, enhanced by chakra, give him an edge over his magic - using opponents. And in the end, he could end up changing the very nature of the Grand Magic Games with his unorthodox style.
If Naruto joins the Grand Magic Games in fanfiction, he would bring his unique fighting style. His chakra control could be adapted to deal with magical attacks. He could also learn new magic skills from the other participants. His positive attitude would likely influence the overall atmosphere of the games as well.
In this fanfiction, perhaps the Grand Magic Games are altered due to the presence of Naruto characters. For example, there could be new events that test both ninja skills and magic. Sasuke could use his Sharingan to counter some of the illusions created by Fairy Tail mages. And characters like Erza would be intrigued by the different fighting styles of the Naruto universe, leading to some epic battles and exchanges of techniques.
It could be someone who also wants the magic book. Maybe a rogue ninja who believes the power in the book can make him the most powerful in the world.
It could be a rogue wizard who wants to steal the power of the Grand Sorcerer. He might be jealous of the Grand Sorcerer's abilities and wants to use that power for his own dark purposes.
It could be someone from the Naruto universe who doesn't like Naruto's newfound fascination with Aku. For example, Danzo might see Naruto's interest in Aku as a threat to the stability of the village and try to stop Naruto from further exploring Aku - related things. So, Danzo could be the main antagonist in this case.