Paul Pogba's 81st minute shot bounced over the line off the crossbar to give France a narrow win in the Group C clash at the Kazan Arena.
A sharp first-half save from captain Hugo Lloris prevented Australia from going ahead through a Corentin Tolisso own goal, and the Spurs keeper warned that France must do better.
However, it was a tough first half for the Les Blues as Griezmann, teenager Kylian Mbappe and Ousmane Dembele fail to spark while it was the yellow-clad Aussie fans who have invaded the Tatar capital in recent days who had most to cheer about.
When asked about the "Bleus" next rival, Peru, Atletico Madrid's number seven had this to say: "We have a hard match against Peru".
Paul Pogba's deflected goal handed France a fortuitous 2-1 victory after Mile Jedinak levelled with a spot-kick, but despite the VAR controversy the Atletico Madrid star was in no doubt the right decision was made in the end.More news: Prince William And Kate Middleton Announce Prince Louis’ Christening Details
Griezmann was clipped by Joshua Risdon, but Cunha did not blow immediately and instead used technology to revisit the incident.
Russian Federation is holding its first time ever edition of the FIFA World Cup, which kicked off in Moscow with a spectacular opening show at the Luzhniki Stadium on the night of June 14. France incidentally is also the second youngest team in the tournament after Nigeria. His team is considered a certainty to defeat Australia in Saturday night's World Cup opener for the two nations and it makes Deschamps uncomfortable. I got a lot of reactions, let's say that out of 10 people seven said it was a penalty and three said no penalty.
Luka Modric scored the penalty kick, sealing the win for Croatia, and putting them to the top of the standings in Group D.
We faced a good Australian team that has played well.
"He is a great player with great potential and has got what it takes".
"We all have to raise our game now and step by step we need to build our confidence and our momentum". Then I saw him look at the VAR and in this moment I knew he would award us a penalty.