Question

Which sentence is written correctly?

Answer 1

From what I know, answer B is correct, because I usually don't see people put quotations around foreign phrases.

However, if B turns out to be wrong my second suggestion would be one where the quotes are only around the phrase in French.

Answer 2

The answer to your question would be that the sentence that is written correctly is the following one: I replied that the new music teacher had a certain "je ne sais quoi."

You should use quotation marks for foreign words that are not understood universally. What is more, AP style also recommends explaining the meaning of the word.