Maybe Castle realizes he can't live without Beckett and confesses his love at the last minute, which stops the wedding. For example, he could show up with some big revelation about their relationship that makes Beckett question going through with the wedding.
In the fanfic, perhaps Castle and Beckett have some unresolved feelings that resurface just before the wedding. They might have a moment of intense eye contact or an accidental encounter where all their old emotions come flooding back. Castle, acting on impulse and true love, stops Beckett from making a big mistake by getting married to someone else.
The main characters are Castle and Beckett, obviously. Castle is likely to be the one who intervenes in Beckett's wedding. Beckett is the one whose wedding is being stopped.
The fanfic could start with Castle and Beckett already having a baby. They are adjusting to their new life as parents. Beckett might struggle a bit with the lack of sleep and trying to balance work and motherhood. Castle, on the other hand, is loving every moment of being a father. He writes a new book based on their experiences of having a baby. Meanwhile, they also have to deal with some family drama, like an over - eager relative who wants to be too involved in the baby's life. But through it all, their love for each other and for their baby only grows stronger.
Perhaps in the fanfic, Beckett bends over in a metaphorical sense, like she's going out of her way to support Castle. It could involve her putting aside her pride or her own goals to help him with a case or a personal matter. For example, she might be willing to take on a dangerous undercover assignment that she normally wouldn't just to protect Castle or further his investigation.
One possible plot could be that Castle sees Beckett with Josh and it makes him realize his true feelings for her. He might then start to compete for her attention in a humorous and endearing way, like writing a new novel inspired by his jealousy and love for her.
Perhaps their daughter has a special talent that gets her involved in a dangerous situation. She could be a prodigy in computer hacking, and while trying to help her parents on a case, she uncovers a secret that puts her life in danger. Castle and Beckett then have to race against time to protect her while also solving the case.
Perhaps the man is a new partner Beckett has been assigned to work with on a case. Castle sees them together and his insecurities get the best of him. He starts imagining all sorts of things, like Beckett replacing him in her life. However, in the end, it turns out that Beckett has no romantic feelings for the other man and Castle realizes he overreacted.
Maybe he's afraid of losing her because she's his partner and they've been through so much together. Their relationship is very important to him.
Maybe he saw Beckett spending a lot of time with another man without knowing it was for a case. Castle is a bit of a jealous type, and he might overreact to normal interactions.
It could be that Castle is overprotective. He loves Alexis so much that even the slightest sign of Beckett not being on the same page as Alexis in Castle's eyes makes him think Beckett hurt her. Maybe Beckett gave Alexis some career advice that Castle thought was too pushy.
Well, it could be that they meet at a summer camp. Beckett is the shy girl who loves to read mystery books in the corner, and Castle is the adventurous boy always getting into little pranks. They might team up to solve a small mystery at the camp, like who stole the counselor's whistle. This initial meeting could plant the seeds for their future relationship as crime - solving partners.