Depending on where you are from, Australia can indeed refer to a continent but this one only includes Western Papua, Papua New Guinea, Tasmania, Australia itself (as a country) and a few small islands. It doesn't include New Zealand

New Zealand is part of Oceania. I invite people that come from this part of the world to correct me if I'm wrong.
You speak French. Are you from France or from another French speaking country? Because I'm from the French part of Belgium and I've never heard someone say that Australia is a continent here. And I'm pretty sure that in France they also use the word Oceania to talk about the continent.