Not ALL over Europe. In Iceland, for example, "fyrsta hæð" is 1st floor, which is at street level (used interchangeably with "jarðhæð" = ground floor).
Interestingly, this is despite the fact that similarly to Hungarian, the word "hæð" means both floor/level and elevation (and hill). So "first elevation" is no elevation.
The Hungarian word "emelet" comes from the verb "emel", which means "to raise/to elevate".
The "-et" is a suffix which makes a noun from the verb.
So "emel+et" already includes, that the floor is "elevated". It means that the first "emelet" necessarily is the one above the ground-floor.
It also means that the floors under the ground-floor should be called "szint" (just like in "földszint").