Mahut, ranked 66 in the world and who has struggled with thigh pain at this year's Wimbledon, is joined for the World Group quarter-final clash in London by Richard Gasquet (world number 20), Gilles Simon (13) and Jo-Wilfried Tsonga (12).
Pierre-Hugues Herbert, who has played doubles with Mahut, was named as replacement in an official team statement on Tuesday.
Monfils, the world number 18, lost a five-set thriller to Simon at Wimbledon on Saturday, and said after his third-round defeat he did not expect to be picked.
"Quite honestly, I don't have a place in the Davis Cup," he told reporters. "There's an impression that I can play well on grass, but it's nothing but an impression."
The Davis Cup tie takes place at Queen's Club in west London between July 17-19.
(Reporting by Andrew Callus and Gregory Blachier, editing by Stephen Wood)
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