One possible plot could be that Kol and Elena meet by chance in a place outside of Mystic Falls. They initially clash due to their different personalities and pasts. Kol is intrigued by Elena's tenacity and her kind heart despite all she has been through. As they are forced to spend more time together, perhaps because of a common threat, they start to understand each other better. Elena begins to see Kol not just as one of the bad guys but as someone with his own complex story. Their love could develop gradually as they share their secrets and fears, and finally, they realize they are in love.
Maybe in the fanfiction, Kol returns to Mystic Falls with a new outlook on life. He crosses paths with Elena, who is still dealing with the aftermath of her previous relationships. Kol starts to court Elena in his own unique way, which at first annoys her but then starts to charm her. Their love story could involve them going on adventures together, away from the drama of the Salvatore brothers and other vampires in Mystic Falls. Along the way, they discover that they have a deep connection that blossoms into love.
The plot could start with Kol being cursed or in some sort of trouble, and Elena is the only one who can help him. At first, Elena is hesitant to get involved with Kol, but she can't resist his charm and the mystery surrounding him. As she helps him break the curse, they get closer. They might have some steamy moments while also having deep conversations. Kol shows Elena a different side of the vampire world, and she shows him the value of human emotions. This mutual discovery leads to their falling in love.