What are the franchises if any? Lets avoid franchises composed of a single game, because that is trivial in almost all cases. And let's consider only the main games in the franchise, discarding the spin-offs.
Let's consider spin-offs, games that differ from the main series in either story (if there is a story common to the main entries of the franchise) or gameplay, or both, independently of the consoles the games are on. For example, Uncharted: Golden Abyss despite not featuring any recurrent character besides Nathan Drake, has the gameplay of an Uncharted game, so for all intents and purposes is part of the main franchise.