Well, not exactly the terms "high" and "low" but the corresponding translations.
Let's take for example the Middle Ages. The periodisation in English splits the Middle Ages in 3:
- Early Middle Ages
- High Middle Ages
- Late Middle Ages
However, in Spanish it's splitted in 2:
- Alta Edad Media
- Baja Edad Media
"Alta" means "high" and "baja" means "low". I also understand that this is the case too in Italian and French.
What strikes me is the somehow counterintuitive use of the term "high" to a early period and "low" to a late one. To me, it makes more sense the other way around.
Here some possible etymological reason are discussed (in Spanish), but with no conclusion. The most likely one is that "high" means that, during the first part, some important features of the period rises and prospers (going high) until reaching its peak, giving place to a decadent second part (going low). I wonder if historians support this idea or can give another explanation.
There is also mentioned that the use seems to be relatively new, since Google Ngram suggests it was first used during the 1890's.