Well, Naruto could have the power to communicate with demons on a different level. Instead of just fighting them, he could try to understand their motives. His godlike status could give him the ability to transform his chakra into a form that can purify demons without having to kill them. He could also use his speed and agility, which are already superhuman in Naruto's world, to outmaneuver demons in the Blue Exorcist universe. And his Sage Mode could be further enhanced, allowing him to gather natural energy from the Blue Exorcist world more easily and use it to his advantage.
He would likely have his regular Naruto powers like the Rasengan, Shadow Clones, and his ability to use chakra. But in the context of Blue Exorcist, he might be able to infuse his chakra with exorcist techniques. So, his Rasengan could become a demon - banishing Rasengan. His Shadow Clones could be used to scout for demons in areas that are difficult to access for normal exorcists.