Another idea is that James Potter had some sort of latent magical ability that we didn't know about in the original story. This ability could have manifested itself when the Killing Curse was cast, and instead of killing him, it triggered this hidden power which saved his life. For instance, he could have had the power to absorb and redirect dark magic, which would be a very interesting plot twist in a fanfiction.
In fanfiction, it could be that the caster of the Killing Curse, perhaps Voldemort, didn't fully mean it. There are theories that the Killing Curse works better when there is pure intent to kill. If Voldemort was distracted or his heart wasn't fully in it for some reason, the curse might not have been as effective.
One possibility could be that there was some sort of magical interference. Maybe a powerful magical artifact or a spell was in place that deflected the Killing Curse just enough for James to survive. For example, if there was a hidden protection charm on him that he wasn't aware of.
One interesting plot could be that James, having survived, decides to go into hiding with his family in a more secretive way. He uses his survival as a motivation to become a stronger wizard and starts to train secretly, waiting for the right moment to face Voldemort again.
Perhaps James had some hidden magical ability that he was unaware of until that moment. It could be something that was passed down through his family but had never manifested before. This ability could have protected him from Voldemort's killing curse. Or, it's possible that there was a plot by some other characters to save James. There could have been a group of wizards or witches who had been secretly working to keep James alive because they knew his importance in the fight against Voldemort. They might have used some sort of time - turning magic or a protective charm that Voldemort couldn't break through.
Well, he might see some amazing technological advancements. Maybe flying cars are everywhere and houses can move. He could also meet his descendants and see how his family has grown over the years.
The relationship between Harry and his parents would be completely different. He would grow up with their love and guidance, rather than feeling like an orphan. There would be a much stronger family bond.
One possibility is that Snape has a change of heart. Maybe he realizes that despite their differences, James is a father and a valuable member of the wizarding world. In some fanfictions, Snape might be in a situation where he sees James being wrongly accused, and his sense of justice kicks in to save him.
In this fanfiction, perhaps James Sirius Potter could learn some of the classic pranks the Marauders were famous for. He might get into all sorts of adventures, following in their footsteps and causing a bit of chaos at Hogwarts just like they did.
In some fanfictions, if they survived, they might have changed the whole course of the wizarding war. They could have joined forces with other powerful wizards and witches earlier and potentially prevented Voldemort from gaining as much power as he did in the original story. They might have also influenced the Hogwarts curriculum, emphasizing more on defensive magic against the Dark Arts from an earlier stage.
Well, it could be that James Sirius Potter initially has some misunderstandings about the Order. But as he meets them, he discovers their true values. For example, he could be in awe of the courage of the older members and start to model himself after them. He might also get involved in some secret missions that the Order is planning, adding his own unique skills and perspectives to the group. This could lead to new friendships and alliances within the wizarding world, and potentially change the course of future events in the fanfiction's storyline.
Perhaps James Sirius Potter is on a quest to clear his father's name in some way. He approaches Snape thinking he can get some answers. Snape, on the other hand, has his own grudges and secrets. Their meeting would then be a battle of wits and emotions as they navigate through the past and present issues.
In fanfiction, when James Sirius Potter meets the Dursleys, he might be shocked by their coldness. He could try to understand why they treated Harry so badly. Maybe he'd confront them about their past actions, or he might just observe them quietly to see what kind of people they really are.