General terms:
* Epic
* Saga
* Chronicle
* Tale
* Novel
* History
* Account
* Recounting
* Description
* Exposition
More specific terms:
* Roman à clef: A novel in which real people and events are disguised as fictional characters.
* Bildungsroman: A novel focusing on the moral and psychological development of a protagonist.
* Wuxia: A genre of Chinese fiction featuring martial arts.
* Fantasy epic: A long narrative set in a fictional world with magical elements.
* Historical fiction: A long narrative set in the past, often with fictional characters but real historical events.
* Memoir: A long narrative about the author's own life experiences.
* Autobiography: A long narrative about the author's own life, written by the author.
* Biography: A long narrative about the life of another person, written by someone else.
Informal terms:
* Story
* Yarn
* Tale
* Adventure
The best synonym for "long narrative" will depend on the specific story you are referring to.