James Bond must be one of the only franchises that doesn't have to worry about continuity and canon. They can just cast a new Bond, ignore everything that happened in the previous movies and create a new status quo from scratch.
No, if anything, the majority of film franchises in history have been similarly lax about canon. The way the Bond films do it is the same way earlier long-running film franchises like Tarzan did it, recasting the lead role multiple times over decades and only vaguely pretending to have a continuity. The Universal Monsters films would shuffle the cast around from film to film -- for instance, one film had Lon Chaney, Jr. playing Frankenstein's Monster and Bela Lugosi playing Ygor, and the next had Chaney playing the Wolf Man and Lugosi the Monster -- and played really fast and loose with the continuity and geography, changing the location of Dr. Frankenstein's lab or the geography of the series's events from film to film.
Then there's something like the Pink Panther/Inspector Clouseau films. A recurring character who turned evil and was unambiguously killed at the end of one film was back to life and (relative) sanity in the next with zero explanation, and of course the third film in the series, made without Blake Edwards or Peter Sellers (Inspector Clouseau starring Alan Arkin), was totally ignored by the later Edwards-made films.
Heck, even today, we still see film series that take a relaxed approach to continuity, like the X-Men films, which have a habit of ignoring poorly-received treatments of minor characters and redoing them in completely incompatible ways in later films (e.g. Angel, Trask, Emma Frost, Deadpool, etc.). Or the upcoming new Terminator film that ignores all previous sequels since T2, or the recent Halloween film that ignored every sequel since the first one. Even in today's film series, continuity is a choice, not a mandate.