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.
Well, in most cases, his friends would likely try to rescue him. Sasuke might put aside his differences for a while and join forces with Sakura and the others. They'd probably start by gathering information about the council's motives and the location where Naruto is being held.
Naruto would be angry. He's not the type to just accept being kidnapped. He'd immediately start looking for ways to escape. He might try to use his ninja skills to break free from whatever restraints Orochimaru has put on him.
In many fanfictions where Gil gets kidnapped, it could be for various reasons. Maybe it's by a rival group who wants to use him as a bargaining chip against his friends. For example, in some stories, Uma's crew might be targeted because they are seen as a threat in the Isle of the Lost. Gil, being a part of that crew, gets kidnapped. Writers often use this plot device to create drama and show the loyalty and courage of the other characters as they try to rescue him.
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.
In fanfiction, Naruto has a lot of ways to escape from Akatsuki if kidnapped. He could wait for an opportunity when the Akatsuki members are preoccupied with their internal disputes. Since he has a strong bond with his friends in Konoha, they might be on their way to rescue him. Naruto could also use his unique Uzumaki bloodline abilities, like his strong life force, to endure any torture or imprisonment until he finds a way to get out. He might even discover some secrets about the Akatsuki during his captivity that could be used to his advantage.
The Akatsuki could be potential kidnappers. They are always on the lookout for powerful jinchuriki like Naruto to extract the tailed beasts from them. Orochimaru could also be a kidnapper as he is always interested in obtaining powerful bodies and Naruto's strength would be very appealing to him.
It could be Orochimaru. He has always been interested in Naruto's power and potential. He might kidnap Naruto to try and extract the Nine - Tails' chakra or study his unique Uzumaki bloodline further. Another possibility is a group of rogue ninjas who want to sell Naruto to the highest bidder, thinking his value as a Jinchuriki would make them rich.
One idea could be that Sam is kidnapped by a group of rogue hunters who think he's gone too far in his use of demon powers. They lock him in an abandoned bunker and try to 'exorcise' the 'demon' out of him, not realizing he's in control. His brother Dean has to race against time to find him, following a series of cryptic clues left by the kidnappers.