"Antoine is Antoine, he's our attacking leader and will remain so".
Mathew Leckie was booked for a foul on Lucas Hernandez after 12 minutes, but Australia repelled Griezmann's delivery into the box.
Australia will now play Denmark on Thursday at 10pm AEST.
A result against France looks fanciful, but if they are within touch late in the second half, look for Van Marwijk to inject 38-year-old striker Tim Cahill, who is bidding to become only the fourth player ever to score at four World Cups. Midfielder Aaron Mooy swung in a risky free-kick which took a nick off Corentin Tolisso and nearly crept into the bottom corner for an own goal.
Australia will also be desperate for a positive start, given their last two World Cup campaigns in Brazil and South Africa were all but ruined by first-match drubbings.
After a disjointed first half, the game sparked into life shortly after the interval as referee Andres Cunha awarded a penalty to France after consulting VAR and deciding that Josh Risdon had clipped Griezmann just inside the area.
But with 17 minutes gone Hugo Lloris prevented Australia from taking a surprise lead, making a fine low save after another Mooy delivery had been deflected towards his own goal by Corentin Tolisso.
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Each of them received a special cover design, with Justify's edition pairing up next to a headline that he "joins the immortals". Gronkowski was slow to start, trailing for much of the race, but just like his namesake, he didn't give up.
It was the Manchester United man who scored the winning goal for the Les Bleus in the 81st minute, finding the net via a deflection, to score his team's second goal and give them a 2-1 win.
Teenager Daniel Arzani came on for Robbie Kruse as Australia chased another equaliser, but they were unable to conjure another goal as France held firm for five minutes of added time.
Their sheer depth of talent has made them among the tournament favourites, yet scepticism lingers over the manager's ability to get the best out of his stars. Coach Bert van Marwijk immediately switched to a back four from the three-man defence favoured by his predecessor Ange Postecoglou when he took over in March and has forged a side that looks more compact. We got ourselves back into the game, we felt good.
"We have not played a great game", Deschamps admitted. I cannot blame any of my players, I can only give them compliments.
"I hoped that maybe one time there would be a very honest referee, and in that moment, that he wouldn't go to the video screen", the Dutchman said.
"He needs to do more, and knows it", Deschamsp said.