Well, it's a blend. While it may draw inspiration from historical facts, it likely incorporates creative liberties and fictional elements to make the story more engaging and cinematic.
It is indeed a real story. Samrat Prithviraj's tale has been passed down through history, and the movie attempts to bring that to the screen. Though it may have some fictional elements added for entertainment value, the basic framework is based on reality.
Samrat Prithviraj is inspired by real history. However, in the process of making it into a film or story, certain elements could have been embellished or simplified for better storytelling and audience engagement.
King Prithviraj Chauhan was a great Rajput king. He was known for his valor and chivalry. He ruled over the kingdoms in northern India. Prithviraj was an excellent warrior and was highly respected. He had many battles against the invaders, most notably against Muhammad Ghori. In their first encounter, Prithviraj Chauhan defeated Ghori. However, in the subsequent battles, due to various reasons including betrayal, he was finally defeated.
Prithviraj Sukumaran has been quite focused on his work in the film industry. There could be speculations about his relationships, but without any official statements from him, it's difficult to define a clear 'love story'. Maybe he prefers to keep his personal affairs away from the media glare and let his work speak for itself.