They might be quite amused. For example, Will Graham might be intrigued by how others perceive his complex relationship with Hannibal. He could find some fanfictions that really dig deep into his psychological turmoil in a way that surprises him.
Typically, it is legal. Fanfiction exists in a bit of a grey area legally, but for the most part, as long as it's non - commercial and not causing harm to the original brand or creators. The creators of Hannibal might not actively promote fanfiction, but they also don't usually go out of their way to stop it. So, if you're just enjoying the fan - created stories, you should be in the clear.
Some characters like Jack Crawford might be dismissive. He is a no - nonsense FBI agent and might think fanfiction is just a waste of time and not in line with the real investigation and profiling work he does. So he would probably just roll his eyes and move on.
One good source could be Archive of Our Own (AO3). It has a vast collection of fanfiction for various shows, including Hannibal. There are different genres and ratings to choose from. Another option might be FanFiction.net, though the interface might not be as modern as AO3 but still has a lot of content.
One character that would be interesting to include is Abel Gideon. He was already a part of Hannibal's world, and in a time - travel story, he could have a different role. Maybe he travels with Hannibal or is sent to a different time to hunt him down. Also, Freddie Lounds could be a great addition. She's always looking for a good story, and Hannibal's time - traveling would be the ultimate scoop. And then there are the victims. What if some of the victims from different time periods were able to come back and haunt Hannibal? That would add a spooky and interesting element to the fanfiction.
There was Hasdrubal, who was related to Hannibal. He also played an important role in the military campaigns against Rome. Another was Scipio Africanus. He was a Roman general who ultimately faced off against Hannibal and was a key figure in the Roman response to Hannibal's invasions.
At first, Will would be in shock. But as time passes, he would start to analyze Hannibal's motives. He is a profiler, after all. He might try to use his psychological knowledge to manipulate Hannibal in return. He could also go through periods of anger, resenting Hannibal for taking away his freedom. And there might be moments of confusion as he tries to figure out if there is any part of Hannibal's actions that could be considered 'caring' in his warped way.