The term you are looking for seems to be “Taxonomy”, category and post_tag are base taxonomies, but you can register more taxonomies, depending on the needs.
Right now, you are in need of 2 taxonomies, “hero” and “franchise”, once registered, you can affect them to a range of post_type.
I don’t know if your “movie” is a CPT (Custom Post Type), but it should probably be.
(Edit) Forgot to give you some link in the Codex:
https://codex.wordpress.org/Function_Reference/register_taxonomy