• “J’ai hâte d’être en vacances”

or

• “Je suis impatient d’être en vacances”

or their informal equivalent:

• “Vivement les vacances!”

I personally would not specify “Summer” in the french translation

I’d say:

Ah, comme j’ai hâte d’être en vacances !

Les grandes vacances me tardent ! == Vacation cannot come/arrive soon enough!

Des vacances relaxantes, voilà ce qu’il me faut !

Not the same phrasing, but essentially the same idea:

How do I say in French 'I can't wait to see them!' ?

“Vivement les vacances!” is clearly the most common.
If you really want to precise which vacation you mean, I would say that “Vivement les grandes vacances!” is adequate, as the summer holidays are the longest of the year.