I interpret what Carnelian is saying is that a native German speaker would not use the phrase "Do you have Tuesday free", though native English speakers would. I expect that is why the translation is noted as incorrect.
I answered as an American speaking German instead of a German speaking German.
It's just the way they say it. Literally do you have free (time on) Friday.
I believe there a tendency of putting time markers forward in German sentences. I read somewhere that the typical order of descriptions is TOMP: time, object, mode (i.e., how) and place -- i.e. time goes first.
EDIT: actually, in this particular case "frei" is part of the separable verb "freihaben", so it must go to the end of the sentence.
I am guessing that an English speaker immediately assumes that the sentence corresponds to English "Do you have Thursday free", which is not a particularly elegant but still acceptable way of asking "Is your Thursday free?".
In other words, we are fooled into thinking that "frei" is an adjective, not a part of a separable verb.
The direct translation is a much better fit in English. Without context, the sentence above means multiple things.
If I was asking this question it would be "are you free on Tuesday" or "do you have Tuesday free" - which are both near direct translations.
Asking if someone is "off" would almost always only relate to someone who is rostered "on" to something.
So it seems freihaben is the verb here and follows the declension rule for separable verbs: https://dictionary.cambridge.org/dictionary/german-english/freihaben