If Robert Baratheon loved Cersei, it might have changed the course of many events. Their relationship could have affected how they ruled, and potentially influenced the fates of other characters. Maybe there would have been more harmony within the royal family.
If Robert Baratheon married Cersei in fanfiction, it's possible that their children's fates would be different. Also, it might affect the alliances and rivalries among the noble houses. The story could take many unexpected turns based on this alternate setup.
It could have led to a very different power dynamic in Westeros. Maybe Robert would have been more controlled by Cersei, or their relationship could have sparked more political upheaval.
Well, for one, the Lannister influence might not have been as strong. Also, the fate of Robert's children and the succession to the throne would likely have changed drastically.
Perhaps their relationship begins with curiosity. Daenerys has heard of the powerful Robert in Westeros, and Robert is intrigued by this Targaryen with a claim to the Iron Throne. As they communicate more, they find common ground in their desire for a just Westeros. They might start to fall in love slowly as they share their dreams and fears, and work towards building a better future for the Seven Kingdoms.
Good fanfiction about Robert Baratheon also needs to capture the essence of the world he lives in. It should include the political intrigue, the power struggles, and the cultural aspects of Westeros. If it can tie in his actions as king with the greater political landscape, like how his decisions affected the different houses, it makes for a great read. Also, delving into his vices, like his drinking problem, and how it impacts his rule and those around him is a plus.
One idea could be a story where Robert Baratheon discovers Jon Snow's true parentage earlier. This could lead to a complex relationship where he sees Jon as a potential heir or a powerful ally. He might take Jon under his wing, train him in the ways of leadership and warfare, much like he did with Ned Stark's other children.
Power is a common theme. Fanfictions often explore how Robert wields his power as king, whether he uses it wisely or misuses it. Another theme is love and lust, like his relationship with Cersei and how that affected his rule.
One possible fanfiction could start with Robert Baratheon as a young man. He is full of ambition and dreams of a united Westeros under his rule. He trains hard in combat, his sword becoming an extension of himself. He meets his future friends, like Ned Stark, during these formative years. They share tales around the campfire and make grand plans for the future. As he grows older, he participates in battles, his victories making him more and more renowned. His charisma draws people to him, and soon he is seen as a natural leader. But with power also comes temptation, and he has to face the challenges of politics and intrigue that come his way.