How to create a camera that follows the player, but on rails?

I’m sorry if this has been asked before, but now matter what keyword I put in, I couldn’t find a previous question that answers my question.

I’m using the Third Person Template, and I’m hoping to modify the camera so that it follows the player in a predetermined path, not unlike in Persona 4 when the player is at the Samegawa Riverbank or the Central Shopping District. The camera has its rotation and transform set relative to where the player is currently at, and follows the player in a predetermined “rail”. The player has no direct control over the camera.

A video for those who haven’t played P4 before: Let's Play Persona 4 NG #12 Going around the shopping district - YouTube

How do I go about doing this? Thanks.