The immortels in the Académie Française do not cease to étudier the French language while they only used to apprendre it when they were kids.

They could both be correct but apprendre le français is learning French and étudier le français is studying French.
In this sentence the meaning of studying is more in an academic way.

Both are quite technically right. But ‘apprendre’ is more common, ‘j’etudie l’allemand’ has a stuck-up whiff about it..