Both players had seven aces on indoor clay at the Kindarea in Rouen. Chardy dropped his serve once and broke Edmund three times.
Earlier, Dan Evans salvaged some pride by thrashing Julien Benneteau 6-1, 6-2 in the fourth rubber to make it 3-1.
With France safely through to the semifinals after winning Saturday's doubles for an unassailable 3-0 lead, France captain Yannick Noah rested 17th-ranked Lucas Pouille and replaced him with Benneteau.
Benneteau, who played in Saturday's doubles triumph, struggled to compete against Evans in a one-sided match lasting just 43 minutes. The 35-year-old Benneteau, ranked 113, dropped his serve five times and failed to force a breakpoint chance against the 44th-ranked Evans.
France hosts Serbia in September. They have not met since the 2010 final, which Serbia won 3-2 at home.