Well, the plot could start with Orochimaru's sudden attack on Naruto when he's alone. He'd probably use some sneaky jutsu to subdue Naruto. Then, once kidnapped, Naruto would be held in Orochimaru's hideout. Naruto might try to communicate with the snakes there, as he has a way with animals, to find a way out.
If Orochimaru kidnaps baby Naruto in fanfiction, it would likely start a race against time for the Hidden Leaf Village to get him back. The village elders and the Third Hokage in particular would be desperate to rescue Naruto. They might send out their best ninjas, including Kakashi, to track Orochimaru down. Orochimaru, on the other hand, could be planning to raise Naruto as his own weapon, brainwashing him from a young age to be loyal only to him.
Well, Naruto might use his Nine - Tails chakra to break free. He's a tough one. He could also try to outwit Orochimaru with his ninja skills. Maybe he'd pretend to be unconscious and then surprise Orochimaru when he least expects it.
First, Orochimaru would probably use some sneaky tactics to capture Naruto. Once he has Naruto, he might take him to a secret lair. Naruto would be thinking of ways to escape right away.
In a fanfiction where Orochimaru kidnaps baby Naruto, the development could be very complex. Orochimaru could initially plan to use Naruto's Uzumaki bloodline for some powerful jutsu creation. But as Naruto grows, he might show kindness towards Orochimaru's minions, which could start to change the dynamic in Orochimaru's hideout. Back in the village, the absence of Naruto could lead to a shift in power. Some might try to take advantage of the situation while others would be focused on getting Naruto back. Naruto himself could end up becoming a sort of bridge between Orochimaru's world and the Hidden Leaf Village if he manages to escape or change Orochimaru's ways.
In some fanfics, Naruto might use his new and powerful jutsu that he has mastered over time. Maybe he combines his Sage Mode with the power of the Nine - Tails in a unique way that Orochimaru can't counter. For example, he could use the Nine - Tails' chakra to enhance the range and power of his Sage Mode attacks, and then catch Orochimaru off - guard.
One consequence could be a shift in the power balance among the ninja villages. Since Orochimaru was a powerful and feared figure, his death might cause some chaos as his former allies or subordinates try to either avenge him or claim his resources. For example, some of his secret labs and experiments might be up for grabs, leading to potential conflicts.
In fanfic, anything can be possible, so Orochimaru could be Naruto's father. But in the official Naruto storyline, it's not the case. Naruto's parentage is clearly defined as Minato and Kushina. Fanfic writers might be trying to explore a different kind of family drama or a new take on the characters' relationships by creating this unorthodox connection.
One possible fanfic could be about a student of Orochimaru who rebels against his evil ways. This student, perhaps having seen the destruction Orochimaru causes, decides to use the knowledge he has gained in a positive way. He might start by secretly helping the Hidden Leaf Village, using his skills in jutsu and forbidden arts to protect rather than harm.
In some fanfics, Orochimaru can be made Naruto's sensei. Fanfic authors often like to play with the original story's elements and create unique scenarios. They might think that having Orochimaru as Naruto's sensei would lead to a very different kind of character development for Naruto, full of more moral and ethical challenges due to Orochimaru's dark nature.