The tie is scheduled for April 7-9 at the 5,000-capacity Palais des Sports de Rouen, known as the Kindarena, which previously hosted France's win against Israel in 2013.
World No 1 Andy Murray sat out Britain's 3-2 victory over Canada in the last round but has said that he expects to return to the side for the clash with France, who advanced by beating Japan 4-1 in Tokyo.
Britain last faced France in the 2015 quarter-finals and went on to lift the cup after winning that match on grass at Queen's Club.
It will be the 22nd Davis Cup tie between the countries, but the first to be staged on clay since 1978.
The surface may take some adjusting to because the match will get underway the week after the Miami Open, which is played outdoors and on hard courts.