One possible storyline could be that Kol and Elena's relationship starts in a rather unexpected way. Maybe they are forced to work together to defeat a common enemy in the supernatural world. During this time, they gradually develop feelings for each other. And when they find out Elena is pregnant, they face a lot of challenges. Some vampires might oppose their union because of Kol's past actions. But they decide to fight for their family and the future of their baby.
Caroline would probably be very shocked at first. She might have some concerns about Kol's intentions, but seeing how much he loves Elena and how excited they are about the baby, she would gradually come around. Stefan would be more reserved in his reaction. He would be worried about Elena getting hurt, but he would also respect her decision. Damon, on the other hand, would be more vocal. He might make some snide remarks at first, but deep down he would also want Elena to be happy. Bonnie would be practical. She would offer to use her magic to make sure Elena has a safe pregnancy and that the baby is healthy.
The Salvatore brothers might be a bit protective at first. Damon would probably be skeptical about Kol being in the picture, but over time he'd warm up to the idea for Elena's sake. Stefan would be more accepting right away and offer his support. Bonnie would be excited and use her magic to make sure the baby is safe. Caroline would be all over helping with baby clothes and advice. As for the Mikaelson family, Klaus might see the baby as a way to strengthen his family's hold in the supernatural world, but also be protective in his own way.
One idea could be that the baby has special powers due to Kol and Elena's unique heritages. For example, it might be able to control both vampire and witch magic in a new way. Another plot could involve the baby being a target by various supernatural forces who either want to use its power or destroy it out of fear. And perhaps the baby's existence could bring about a new era of peace or chaos in the supernatural world, depending on how it's raised and the choices it makes as it grows up.
They could develop a shared hobby. For instance, they both get into painting and use it as a way to express their emotions and connect on a deeper level. It would be unique because it shows a side of them that's not related to their supernatural natures.
In many 'The Vampire Diaries' Kol and Elena fanfictions, their relationship can be quite complex. Kol is often depicted as a wildcard, and his interactions with Elena can range from intense and dangerous to oddly alluring. Some fanfictions might explore a forbidden - love - type scenario, where Kol's vampiric nature and his family's history with Elena's friends create barriers. However, they also might find common ground in their mutual experiences of being caught up in the supernatural chaos of Mystic Falls.
The other vampire clans might be antagonists. They could see the baby as a threat to the vampire hierarchy or fear that the baby will have powers that could disrupt the balance among vampires. For example, the Originals' siblings who don't trust Kol might try to stop Elena from having the baby.
One possible plot could be that Kol kidnaps Elena to use her as bait for his enemies. He might think that by having Elena in his custody, her friends, especially the Salvatores, would come to rescue her and he could then ambush them. Another idea is that Kol has some sort of vendetta against Elena because of her connection to the doppelganger bloodline. So he kidnaps her to extract revenge on the entire line.
One common theme is forbidden love. Since Kol and Elena might be from different 'worlds' or groups within the show's lore, their relationship can be seen as something that goes against the norm. Another theme could be passion. The kiss is often a moment of intense passion that drives the story forward.
Another character that could be important is Elijah. He is often the voice of reason among the Originals. He might try to guide Kol in his relationship with Elena, or he could be against it if he thinks it will bring trouble to their family. So in this fanfiction, he could be a key figure in the development of the Kol - Elena relationship.