Caesar Flickerman was always the face of the Hunger Games in the Capitol. In my fanfiction, he starts to question the morality of the Games. One day, while preparing for an interview, he looks at the tributes' files and sees the pain and suffering they've endured. He decides to subtly try and change public perception during the interviews, dropping hints about the inhumane nature of the event.
An interesting plot could be that Caesar Flickerman discovers a conspiracy within the Capitol to manipulate the Hunger Games even more than usual. He uncovers that certain powerful people are choosing specific tributes to ensure their own political gain. He has to decide whether to expose this or keep quiet to protect his own position.
For Caesar, you can show his ambitious side not just in politics but also in his relationship. He could be determined to make Cornelia the happiest woman, seeing it as another conquest. For Cornelia, emphasize her intelligence. She can be the one who gives Caesar good advice on political matters from time to time.
Julius Caesar's story is based on actual history. While some details might have been embellished or simplified for storytelling purposes, the main events and his existence are factual.