The island group shown on the map is just Kerguelen though, and the other parts of the French Southern Lands do not belong to Antarctica (even Kerguelen is a stretch, about as far south as Paris is north) except for Adelie Land, which is a different answer on the quiz anyway. So Kerguelen should definitely be accepted imo, or even excluded.
If Kerguelen is on the quiz, the South Orkneys, South Shetlands, Scott Island and Balleny Islands should be as well, all of which are more southern.
There seems to be some confusion - the French territory Southern and Antarctic Lands has 5 districts, including Adélie Land, their claim on the Antarctic continent itself - unrecognised as are all such claims - as well as island territories recognised as being under French sovereignty, whether Antarctic - Kerguelen - or non-Antarctic eg 'Iles Éparses' and the Crozet, St Paul and Amsterdam islands. The only correct answer here should be 'French Southern and Antarctic Lands'.
I wanted to make this quiz too
If Kerguelen is on the quiz, the South Orkneys, South Shetlands, Scott Island and Balleny Islands should be as well, all of which are more southern.