It could be a time - travel or multiverse - hopping scenario. A character from Hunger Games discovers a way to travel to different universes and ends up in the Marvel universe. There, they are attracted to a particular character, say, Captain America. The differences in their worlds and values create an interesting dynamic for their love story, with the Hunger Games character teaching Captain America about the harshness of Panem and Captain America showing the Hunger Games character the ideals of heroism in the Marvel world.
Well, one way could be a crossover fanfic. Imagine a character from Hunger Games being thrown into the Marvel universe and falling in love with a Marvel hero or anti - hero. For example, Katniss could end up in New York City during an Avengers battle. She might meet Hawkeye and they could develop a relationship as they fight side by side against a common enemy that somehow ties in elements from both universes, like a villain using the Capitol's technology.
Perhaps a love story between a mutant from the X - Men (part of Marvel) and a rebel from Hunger Games. The mutant could have powers that are both a curse and a blessing in the Hunger Games world. They meet when the mutant is trying to escape from some anti - mutant group and lands in Panem. There, they meet the rebel and they start to understand each other's struggles, which eventually leads to love.