It was a far cry from the insipid performance during last month's 0-0 draw away to Georgia and the woeful first half against Belarus, where France was in total disarray and trailed 1-0 before responding with four second-half goals.
In recent years, France has often been jeered by its home fans at matches. But on Friday night, the hard-to-please crowd rose to their feet at Parc des Princes to applaud them off the pitch after a feast of attacking football.
"People want to be thrilled and to feel sensations," Deschamps said.
There was another welcome sight: Karim Benzema scoring again for the first time since June last year.
After ending his 15-match run without a France goal, Benzema was quick to play it down.
"I knew it wouldn't last 10 years. But once again, the most important thing is the team, not me," the Real Madrid striker said. "It had been a while. I'm very happy but it's not just about my goal. You have to talk about the match, how spectacular it was. If it was 6-0 then that's down to the whole team."
Benzema remains under pressure, however, and in the last two games has lost his starting place to Arsenal's Olivier Giroud, who scored twice and led the line brilliantly against the Australians with his touch and link play.
"Giroud must take credit," Deschamps said. "He started against Belarus and yesterday, and he also scored."
Giroud said in an interview leading up to the game that he felt he had earned the right to start at No. 9.
"We scored six, that's why I'm smiling today, and because I scored twice. I won't lie," Giroud said. "I have a lot of belief in this team."
Giroud clearly thrived with the recalled Samir Nasri playing behind him in a playmaker role like when Giroud scored on his debut against Germany in February, 2012.
But with a goal and three assists, Franck Ribery underlined his status as France's inspirational player. The 30-year-old winger is in the best form of his career for Bayern Munich and France is reaping the benefits.
However, that does make France look a bit predictable at times, as many of the attacks stem from the left, where Manchester United defender Patrice Evra likes to combine with Ribery.
"He's one of the best players in the world, and the more he gets on the ball the better," Deschamps said. "Most teams have a favorite system. The important thing is to keep the balance."
Deschamps got a further boost with center half Laurent Koscielny returning to training on Saturday after missing Friday's game because of a calf injury.