"The Federal Office has today decided to terminate the mandate of captain Arnaud Clement," the FFT said on Twitter.
"The Federation welcomes his commitment over the past three years at the head of the France team."
The 37-year-old former Wimbledon doubles champion helped guide France to last year's Davis Cup final where they lost 3-1 to a Swiss side featuring Roger Federer and Stan Wawrinka in Lille.
This year France were knocked out in the quarter-finals by Great Britain at Queen's Club in London.
French national technical director Arnaud Di Pasquale admitted that former world number three Noah was among the frontrunners with an announcement expected next week.
It would be a third spell with the French team for Noah after winning the Davis Cup as captain in 1991 and 1996.
"It's an open secret, Yannick has shown an interest in returning," said Di Pasquale.
"It's true that talks with Yannick are quite advanced. It's a long process as well, we've had numerous discussions but nothing has been rubber stamped.
