I have used folksonomy tags to track franchises before. Said tags can organize across different entity types.
I did create a JIRA ticket a few years ago to add “Franchise” as an entity type, but as of this writing it has gone nowhere.
I don’t know if we should call it Franchise, though. It sounds quite like McDonald’s and highly commercial crap stuff like that.
Maybe it should be called Topic or Theme or Category… or Franchise if it’s what people are used to (I’m not really used to this, but I’m not using English in daily life).
Is this actually a question for the MusicBrainz database, or a question for your own files? I have plenty of proprietary tag fields in my own files that would be impossible to be stored in MusicBrainz.
There is not really a “proper” tag for franchise. The 2 most popular approaches I have seen are,
The “Grouping” field as written by iTunes (also known as “Content Group”)
Repurposing the “Album Artist” field to contain the franchise as a fake artist