Which is the correct one?

Are you free on Sunday is correct.
It is because the grammar of 'Do you free on Sunday?' is wrong.

1. Free is an adjective and it cannot be used in a question started with "do".

2. Questions started with "do" should match with verb.

3. The reply of 'Are you free on Sunday?' is "Yes, I am free (on Sunday)" or "No, I am not free(on Sunday)"

i.e. 'Are you free on Sunday?' is correct

'Are you free on Sunday?' is correct.

Because free in this sentence is adjective, before adjective of course is word to be, i.e. is/are/were...etc.

If it's verb, then you should ask with DO. e.g. Do you buy the apple?