Mini Games are used as transitions between several chapters in Fran Bow.
Chapter 1[]

Fran in the maze.
At the end of Chapter 1 Fran must navigate a maze in order to escape Oswald Asylum. The maze is patrolled by numerous Kamalas that will attack Fran if she does not keep her distance from them. Being attacked by a Kamala forces Fran to restart the maze, hence she must avoid them while searching for the exit.
Fran will enter the maze in the lower right corner while the exit, a sewer pipe, can be found in the upper left corner.
Chapter 2[]

Fran riding the Toad.
At the end of Chapter 2 Fran and Mr.Midnight must ride the Toad in order to escape from Clara and Mia's Cottage.
This minigame resembles Frogger, a classic game from 1981 that resembles a frog crossing the road, another similarity is that we play as a toad in the minigame while the main character of Frogger is a frog.
Chapter 3[]

Fran and Mr.Midnight running away from a Terrible Creature
At the end of Chapter 3 Fran must pass through the Secret Woods in order to come back into her reality from Ithersta, while passing through the Secret Woods, Fran has to escape from "Terrible Creatures" according to The Great Wizard, he also notes that they're quite slow.
While running from a Terrible Creature, Mr.Midnight will run ahead of Fran and jump when needed, allowing the player know when to jump in order to avoid obstacles.