Guy Noves refused to discuss his future in the aftermath of the 18-17 defeat to South Africa.
France fell to their third straight defeat in the November series, following two defeats to New Zealand last week.
French federation President Bernard Laporte had challenged France to achieve three wins from four in the series.
Noves told Reuters: "My future, I won't answer questions about it. I don't ask myself questions about my future.
"With all due respect, you're tiring me with this question.
"If my future depends on defeats, I can't control that. You should ask the questions to the people who own my future."
Despite the positivity surrounding the new half back pairing of Antoine Dupont and Anthony Belleau, France are yet to win during the November internationals and will have one final opportunity against Japan next weekend.