There's only one onyomi reading for kanji 学 and its "gaku", where did "gatsu" come from?
Historically, 学校 was spelled in kana -- and pronounced as something like -- がくかう. Regular sound changes resulted in modern がっこう:
- In the ～くか～ in the middle, the //u// sound was unstressed, leading to it gradually being omitted.
- The //au// vowel combination on the end shifted from //au// (like English ow!) to //ɔː// (like English awe) by the early 1600s, as demonstrated by the 1603 Nippo Jisho (Japanese-Portuguese dictionary). This then merged with //oː// (the long "O" sound) between then and the early modern period.