One possibility is that the Akatsuki members might try to extract information from her. Since Naruto has a lot of knowledge about the Hidden Leaf Village. Maybe they want to know about the Nine - Tails inside her. However, Naruto is very stubborn, so she would likely resist their interrogation attempts.
Another scenario could be that some members of the Akatsuki start to have a change of heart after kidnapping her. Naruto has a way of influencing people with her positive attitude. For example, Sasori might start to question his loyalty to the Akatsuki after seeing Naruto's determination and kindness. And this could lead to internal conflicts within the Akatsuki group.
Well, in a fanfiction like this, Naruto might be in for a tough time. Pan could be from some other universe and have her own motives. Maybe she wants to use Naruto's powers for her own gain. It could lead to a really strange adventure where Naruto has to figure out how to escape and get back to his own world.
Perhaps Itachi sees Naruto as a key to unlocking some hidden power or knowledge. He could be planning to train Naruto in some way, away from the influence of the village. This would be a strange turn of events considering their previous interactions.
Perhaps Konan and Naruto would go on a journey together. They could explore new places, and Konan would get to experience the world outside of Akatsuki's influence. Naruto would introduce her to his friends and the way of life in Konoha. Konan might also start to learn some of the Konoha ninja techniques and incorporate them with her own. Their relationship could grow stronger as they face various challenges together, like dealing with rogue ninja or helping villages in need.
Well, in such a fanfiction, Sakura might be used as a bargaining chip. The Akatsuki could try to exchange her for something valuable, like secret jutsu. Or they might want to extract information from her about Konoha's defenses.
Naruto getting kidnapped by Orochimaru would be a really dangerous situation. Orochimaru could start by putting Naruto in some sort of chakra - suppressing device. This would limit Naruto's ability to use his Nine - Tails power. Then, he might try to implant some of his cursed seals on Naruto, which would give him more control over Naruto. But Naruto has his own allies within himself. The Nine - Tails, despite their rocky relationship, might help Naruto out in this situation. Also, Naruto has the memories of all the people who care about him. He'd draw strength from those memories and keep his hope alive, waiting for the moment when he can break free and return to his friends and the village.
Well, one possibility is that the Fem Kyuubi might take Naruto to her lair. Maybe she has some strange motives like trying to understand the power of the Nine - Tails within Naruto better. She could be planning to train him in a different way or perhaps use him as a bargaining chip against the Hidden Leaf Village.
Well, Naruto getting the Rinnegan and joining Akatsuki is a wild concept. It would lead to some really interesting battles. For example, a fight between him and Sasuke would be on a whole new level. Since Naruto has the Rinnegan now, he might have new jutsu and abilities that Sasuke wouldn't be expecting. In Akatsuki, he could also learn a lot about the darker side of the ninja world that he didn't know before. But this would also put him at odds with Kakashi and other Konoha ninjas who have always trusted him. And who knows, maybe he could end up reforming Akatsuki into something good instead of a group of villains.
In fanfiction, if Naruto gets kidnapped by Akatsuki, he might be used as a bargaining chip. The Akatsuki could try to exchange him for something valuable like the Nine - Tailed Fox's chakra. Or they might try to extract the Nine - Tails from him forcefully. Naruto would surely put up a fight though, using his Rasengan and other jutsu.
If Sakura gets kidnapped by the Akatsuki in fanfiction, Sasuke could also get involved. Since he has his own history with the Akatsuki, he might use his knowledge to track them down. Also, Sakura herself could be trying to find a way to escape from within. She's a strong kunoichi, after all. She might be gathering information about the Akatsuki's plans while being held captive.
Female Naruto joining the Akatsuki in fanfiction would be really interesting. Firstly, her relationship with other members would be complex. She might have a strange bond with Itachi, as they both have a sense of protecting something important. Secondly, she could use her talk - no - jutsu in a new way among the Akatsuki members. Her energy and positive attitude could either be a nuisance or a source of inspiration for them. And her combat skills would definitely make her a force to be reckoned with in the Akatsuki.