Power play. Snape may want to show his authority over Harry. He has always had a complex relationship with Harry, and in some fanfiction, he could hold Harry to assert his dominance and prove that he is still a force to be reckoned with in Harry's life.
Love for Lily. Since Harry is Lily's son, Snape might hold Harry to keep him safe out of his lingering love for Lily. He doesn't want to see Harry come to harm, so he takes extreme measures like holding him in a secure place.
One possible motive could be that Snape is still deeply influenced by his loyalty to Voldemort in this fanfiction. Maybe Voldemort has some hold over him that forces him to do the unthinkable. Another reason could be a misunderstanding. Snape might believe that Harry has turned to the dark side or is about to, and he decides to take preemptive action to stop what he thinks will be a great evil.
Another reason could be a build - up of years of pent - up anger and frustration. Snape has been harsh on Harry throughout his years at Hogwarts. Harry has had to endure Snape's unfair treatment, and all of that negative emotion could explode in a moment of extreme stress or danger, leading him to stab Snape.
There's a chance he'll meet other outcast wizards. These wizards might have been shunned by the wizarding world above ground. They could be very different from the wizards Harry is familiar with, perhaps having their own unique styles of magic. They might initially be hostile to Harry, seeing him as an outsider from the 'normal' wizarding world, but later they could become his allies. They might also know secrets about the underground world that could help Harry in his future battles or quests.
Hermione would surely be one of the first to help. She is highly knowledgeable in magic and would likely try to use a healing spell or find a potion to stop the bleeding.
One challenge could be the inter - house rivalry. Slytherin and Gryffindor have a long - standing history of not getting along. So, Harry's decision to be involved with Daphne, a Slytherin, might face opposition from his Gryffindor friends. They might not understand why he is choosing a Slytherin girl over someone from their own house.
In fanfiction, Harry Potter going to France could lead to an adventure where he gets involved in a mystery related to a powerful French magical artifact. He'd have to team up with local wizards to solve it and in the process learn about the rich history of French magic.
He could have an adventure in the Spanish wizarding markets. There would be all sorts of strange and wonderful magical items for sale. He might find a unique wand or a potion ingredient that's not available in England.
Well, 'harry potter holds ron fanfiction' could be about a fan - created scenario where Harry is in possession of a piece of fanfiction related to Ron. This could lead to all sorts of interesting plot developments within the fan - created world. For example, perhaps Harry discovers something about Ron through this fanfiction that changes their relationship in the story.
Snape could be very cold at first, but then his natural instinct as a healer (since he is quite good at potions which are often used for healing) might take over. He might give Harry a potion to ease the pain and start to patch him up. All the while, he would probably be scolding Harry for being so reckless and getting into a situation where he got injured.
Maybe Snape is being controlled by some dark magic or a curse that makes him act this way against his normal nature.