You could also call it a comical narrative. It implies a story that's designed to make people laugh or find it amusing.
A humorous tale could be another way to say it.
Another word for a funny story could be a jesting chronicle. This suggests a story filled with jokes and light-hearted moments.
A droll yarn. 'Droll' means odd or whimsical in a funny way, and 'yarn' is another word for a story. So a droll yarn is a good alternative for a funny story.
A humorous anecdote. It's a short and often funny account of an event or incident.
Jokes. Jokes are short and humorous tales or statements that are meant to make people laugh, just like funny stories.
Well, 'narrative' is another word for story. It's often used to describe a sequence of events or a tale.
Another option is 'protracted story'. It implies that the story goes on for a considerable time. You might also hear 'drawn-out account' used in a similar way.
Main character. A story usually revolves around the main character. This could be a person, an animal, or even an inanimate object in some cases. In 'The Little Prince', the little prince is the main character. He is the focus of the story, and all the events and interactions are related to him in some way.
Romance. It is a very common alternative word for love story. Romance often implies a relationship filled with love, passion, and sometimes adventure.