One possible plot could be Percy having to overcome some sort of magical or divine interference. Maybe he has to prove his worth to Gaea in a series of trials. Another aspect could be how the other demigods react to this union. Some might be in shock, while others might try to stop it for the greater good.
Obviously, Percy and Gaea would be the main characters. But there could also be other characters like Annabeth. She might be heartbroken at first when she hears about Percy's marriage to Gaea. And then there could be some of the other demigods like Jason or Piper who would be involved in trying to understand what's going on and maybe even stop it if they think it's a bad thing.
Well, it's not as popular as some other pairings in the Percy Jackson fandom. Gaea is a major antagonist in the series, and the idea of her in a romantic relationship with Percy is rather unorthodox. So, compared to more common pairings like Percy and Annabeth, it has a much smaller following.
One great 'Percy Jackson Gaea' fanfiction is 'The Battle Against Gaea's Wrath'. It continues the story after the end of the main series, with Percy and his friends facing new threats related to Gaea. The author does an amazing job of keeping the characters' personalities intact.
One possible fanfiction could be about Percy Jackson having a strange encounter with Gaea's power while in a lemon grove. Maybe the lemon trees are enchanted by Gaea, and Percy has to figure out how to break the spell without getting caught in Gaea's grander plans for chaos.
In the Percy Jackson series, Gaea is a villain, and a love relationship between Percy and her in the context of the original story is very unlikely. However, in the world of fanfiction, anything can be created. There might be some fanfictions exploring such a strange and dark concept, but it would be a very unorthodox take on the characters.
It could be Aphrodite. Since she is the goddess of love, it would be an interesting twist. Percy might initially resist her charm but eventually be won over by her true self. Their marriage could bring a new understanding of love to the world of the fanfiction.
A common theme is redemption. Many fanfictions explore the idea of Gaea being redeemed through her interaction with Percy. Since Percy is often seen as a symbol of hope and goodness in the original series, his influence on Gaea can be a way to show that even the most malevolent beings can change.
Well, it could be a really wild ride. Percy joining Gaea would be such a shock to his friends. They would probably think he's been brainwashed. And Percy himself might be in for a rude awakening when he sees Gaea's true intentions. She could be using him to get to other demigods, or to start a war between the gods and the demigods. He'd have to figure out a way to break free from her influence before it's too late.
One common theme is identity struggle. Since Percy is known as the son of Poseidon in the original, being the son of Gaea in fanfiction makes him question who he really is. Another theme is power and its consequences. With a different origin, he has different powers and has to deal with how they affect him and those around him.