Gasquet and Tsonga had 74 winners, including 21 aces, between them. They finished off the match with their eighth break of the day.
Gasquet opened the series Friday with a 7-6 (7-3), 6-2, 6-2 romp past Nick Kyrgios and Tsonga added on a 6-3, 6-2, 7-6 (7-2) decision over Hewitt.
France was to have gone with the doubles team of Julien Benneteau and Gael Monfils, both ranked in the Top 40 in singles, but French captain Arnaud Clement turned to Gasquet and Tsonga, who are both in the Top 10.
Sunday's schedule has Gasquet playing Hewitt and Tsonga going against Kyrgios but that lineup is likely to be changed.
It was just the fifth time in 15 Davis Cup meetings that France defeated Australian. Before this week, France and Australia last played in the 2001 final when France won its ninth and most recent Davis Cup championship.