In most European countries the ground floor is not considered the same thing as the others. As Wikipedia puts it: "In most of Europe, the "first floor" is the first level above ground level".
We consider and count as floors the "layers" above the ground level. In french for example, the ground level is called "rez-de-chaussée" and the floors above it "XX étage". The ground level is not an "étage" (in American terms, the "ground level" is not considered a floor, and is not counted among the floors).
For this reason, apart from elevator labels nobody calls the ground level "the 0th floor" when speaking/writing.
And even in elevators, O is just used as a convenient way to convey the ground level (since the buttons don't fit much) -- and not everywhere. In many elevators it gets it own designation (e.g. G or GRD or some other national variety).
It's "the ground level" (with different names per country) + "N floors".
A multi-floor building with ground floor + 3 floors can even named "3rd-storey building" in some countries (and the ground level is just taken as granted) -- e.g. une maison à deux étages in the UK --> 3 story building in the US.