Did OR Studied??

Studied is correct. You cannot "do" a language. You can study or speak a language.

In the U.S., we say, "I took French at school" or "I studied French at school". (The latter is more formal.) I would be more likely to say "in elementary/middle/high school" or "in college" than "in/at school."

Cambridge grammar book gives an example with "did".

Is it wrong?

Do (and did) normally mean performing an action, which is why "did French" is confusing because French is not an action. However, do can also mean achieve or complete, so maybe the author is taking "French" as something that can be completed. I often hear this in informal speech: I did track in high school.