Each side won a match, bringing the overall score to 4-1 in France's favour, after Dan Evans beat Julien Benneteau then Jeremy Chardy beat Kyle Edmund.
France had built in an insurmountable lead across the first two days, winning all three matches against Great Britain with two singles contests remaining on Sunday.
A light-hearted first rubber, won 6-1 6-2 by Evans, was punctuated with three members of the French team all playing on the court at the same time.