I think you have already landed on your general term:
1.1 A set of books, periodicals, or other documents published in a common format or under a common title.
‘the first four books in the Toybox Science series’
When referring to a storyline or set of characters that are followed through more than one work, this usage seems to be more common for novels (especially fantasy novels), but it works for films as well.
I would distinguish it from a franchise, which can refer to a series (of films, novels, or what have you), but references the entire commercial enterprise around the series.
1.2 A general title or concept used for creating or marketing a series of products, typically films or television shows.
‘the Harry Potter franchise’
You can see how they are distinguished in an example from the wikipedia entry for The Fast and the Furious
The Fast and the Furious (colloquial: Fast & Furious) is an American franchise based on a series of action films that is largely concerned with illegal street racing, heists and espionage, and includes material in various other media that depicts characters and situations from the films.
Here, franchise refers to the entire commercial enterprise ("an American franchise"), where series refers to the films themselves ("based on a series of action films")