Mauresmo's victory gave the French an unassailable 3-0 lead over a U.S. team missing several of their top players.
The Americans, playing in their 26th final, were chasing a record 18th Fed Cup crown.
France, also Fed Cup winners in 1997, led 2-0 lead after the first day, with Mauresmo beating Lisa Raymond 6-4, 6-3 and Mary Pierce overcoming Shaughnessy 6-3, 3-6, 8-6 in a baseline battle lasting more than two hours.
The French victory was especially sweet for their captain Guy Forget, who became only the second person to lead his country to both Davis and Fed Cup titles, repeating the feat of his compatriot Yannick Noah.
Forget, who first won the Davis Cup as a player in 1991, also captained France to the title 10 years later.
