In such a scenario, Naruto's friends from his own world might also sense his distress somehow and try to find a way to reach the Fairy Tail world to help him. For example, Kakashi could use his Sharingan to track Naruto's chakra signature even across different dimensions. And once they arrive, there could be a clash of different fighting styles between the ninjas and the mages.
Well, if Naruto is badly injured in a Fairy Tail fanfiction, perhaps the Fairy Tail mages would try to heal him using their magic. They have various types of healing magic like Wendy's Sky Dragon Slayer magic which could be used to mend Naruto's wounds.