Well, in such fanfiction, Luffy's character often becomes more aware of his emotions. Usually, he is so focused on adventure and being the Pirate King, but when he falls in love, he starts to think about someone else's feelings. For example, he might be more hesitant to go on extremely dangerous adventures without considering how his loved one would feel.
Some fanfictions also pair Luffy with Hancock. Given Hancock's infatuation with Luffy in the original series, it's not a stretch to develop a full - blown love story. Her powerful status as a pirate empress and Luffy's carefree nature can create an interesting dynamic, with Hancock trying to win Luffy's heart while he is mostly oblivious to her romantic intentions.
Often, it starts with their mutual respect. Luffy respects Robin's intelligence and strength, and Robin respects Luffy's leadership and unwavering spirit. Their relationship then grows as they share adventures and overcome challenges together. For example, in many fanfictions, during a battle where Robin is in danger, Luffy's fierce determination to save her deepens their bond.
Luffy shows his love for Nami in a very unique way. He gives her a great deal of freedom on the ship. He allows her to manage the money, which is a big sign of trust. Also, his constant protection of her is another way. For instance, during battles, he makes sure Nami is safe. He doesn't question her navigation skills and always follows her lead in that regard. His simple gestures like sharing his food with Nami also show that he cares about her in his own Luffy - like way.
Luffy is still alive and kicking in the manga. The story keeps evolving with him at the center of the action, encountering new enemies and growing stronger.