No. Antarctica has no sovereign countries and no permanent human population. The 1959 Antarctic Treaty freezes all territorial claims and designates the continent for peaceful scientific research only.
However, France operates several research stations where French is the working language:
Other nations with stations (USA, Russia, Argentina, Chile, UK, Australia, etc.) use their own languages. English is the de facto lingua franca for international coordination.
So while you'll hear French spoken daily at French bases, there is no "French-speaking country" in Antarctica.