Garcia and Roger-Vasselin beat the pair of Ulrikke Eikeri (31) and Casper Ruud (25) 7-5, 6-4 in an entertaining mixed doubles decider.
The first set was a tight affair until France broke serve to make it 6-5 before holding to win the opener, and then made the only break for a 2-1 lead in the second set.
"Tomorrow is going to be a day off. We are not that young anymore, especially me," playing captain Roger-Vasselin said.
"Tomorrow will just be a day off, try to rest, enjoy Sydney maybe and then come back strong for Saturday's semi-final."
World number 20 Garcia earlier survived a second-set scare to give France the lead with a 6-2, 6-7, 7-6 victory over Helgo.
Garcia looked on course for a straightforward win after cruising through the first set and getting to match point in the second set's tiebreaker, but Helgo, ranked 544 in the world, rallied to make things difficult for the Frenchwoman.
"It was a crazy match. Malene was a player I didn't know but she just hit the ball so well," Garcia said. "I went through all the emotions out there and I had to find a way through. Today it was almost too much, but in the end I got the point.
Ruud, who won his last two singles matches, brought Norway back into the tie with his 6-1, 6-4 win over Adrian Mannarino (35).
World number 22 Mannarino had simply no answer to Ruud's clinical game and the Frenchman only avoided a 'bagel' by holding his last service game of the first set, before improving in the second.
Norway will face top-seeded Poland in Saturday's semi-final in Sydney. Greece and Germany play on Friday to decide who will face Australia in the other semi-final.
