There have been two novellas released for Final Fantasy XIII-2: Fragments Before and Fragments After. The former serves as a prequel to the game, while the latter deals with the game's many loose ends.

Final Fantasy XIII-2 Fragments Before

Fragments Before includes the second Final Fantasy XIII novella, Episode i, as its prologue. The rest of the book deals with setting up the world of FFXIII-2, such as life in New Bodhum up until 3 AF, Snow's departure, the start of the Academy, and Noel's childhood.

Wildly, an official English translation of the book came out in 2019. Alternatively, you can read a summary of the book here on the FF Wiki.

Final Fantasy XIII-2 Fragments After

Fragments After is a much more disjointed story, picking up many different plot threads from FFXIII-2 and providing more context. It goes into detail on the various Yeuls seen through the story, Lightning's time in Valhalla, Snow's journey to 300 AF, Alyssa's battle against her fate, and an exploration of Noel's time with Yeul and Caius. All in all, this is the book that explains a lot of FFXIII-2's more esoteric plot elements.

The book was published in English in 2019. Alternatively, you can read a summary here on the FF wiki.