Just a little correction:
...on Saturdays (I would use on Saturdays to mean something that happens repeatedly.)
She does not have English classes on the next Saturday (or Next Saturday shen won´t have English classes.) I added "next" not to make it ambiguous, one getting in two minds if the statement meant next Saturday or on Saturdays in general.
If we want it with "On Saturday" meaning "next Saturday" we could put it at the beggining of the sentence.
This is my opinion, though. Let´s wait for more comments.
One grammar aside note: The initial letter of names of the days or months are always capitalized. This way we have: Sunday, Monday, Tuesday, Wednesday... And January, February, March, April...