The ninth-ranked Gasquet had little trouble beating teenager Nick Kyrgios 7-6 (3), 6-2, 6-2, and the 10th-ranked Tsonga followed up just as emphatically to dispatch Lleyton Hewitt 6-3, 6-2, 7-6 (2) and improve to 4-0 in head-to-heads against the former two-time Grand Slam champion.
''They were two very good matches,'' France captain Arnaud Clement said. ''They did what they had to do and played the right way.''
Gael Monfils is scheduled to play alongside doubles specialist Julien Benneteau against Hewitt and Chris Guccione in Saturday's doubles, where a win will seal France's place in the quarterfinals against Spain or Germany in April.
But Clement may change his players around.
''Everything's possible for tomorrow,'' he said. ''I have a little idea.''
Australia captain Pat Rafter said France ''were too good'' and that ''Jo played very well.''
Tsonga saved a break-point in his opening service game, before breaking Hewitt in the sixth game with a backhand winner.
Tsonga took both of his break-point chances in a tight second set, and both players saved two break points each in the third.
''He was fighting right until the end, even though I dominated the first two sets,'' Tsonga said. ''I'm happy to have played well and to give France the second point. I've been playing very well for a while now. I didn't have much luck at the Australian Open because I came up against a very good Roger Federer.''
Gasquet was a heavy favorite against a player ranked 162nd, but the 18-year-old Kyrgios competed well in a tight first set where neither player offered a chance on their serve.
He broke Kyrgios' serve twice in the second and third sets and clinched victory on his third match point when Kyrgios' backhand down the line landed just wide.
''The first set was really important for me and then I felt better and then my backhand started to work better,'' Gasquet said. ''It's my best shot so if I want to win games it has to function properly.''
It is the first meeting between the nations since the 2001 Davis Cup final in Melbourne, which France won for its ninth and last title.
Australia has an impressive 28 titles but none since 2003.