"free" can mean that it costs nothing, is not restrained or is not occupied/taken. Take these examples:
"That man is free" (He is not under restraint)
"Is this free?" (does it cost nothing?)
"Is the room free" (free = available)
However, "vacant" ONLY means empty when used to describe an object (colloquially it can mean "stupid" or "unfocused"), and so you can only say:
"Is the room vacant?" (Is it not occupied/empty?)
In speech, however, we would normally say "available", "free" or "empty"
hope this helped!