Australia took a shock lead after Craig Goodwin scored just nine minutes after the match began.
France, whose build-up to the tournament was marred by injuries, saw left-back Lucas Hernandez come off hurt in the move that led to Goodwin’s goal.
However, they recovered to equalize through Adrien Rabiot before Giroud put them ahead with an easy finish in the 32nd minute for his 50th international goal.
Kylian Mbappe got his name on the scoresheet in the second half and Giroud sealed the win to equal Henry’s record tally of 51 goals for France. The win leaves them top of Group D after Denmark and Tunisia drew 0-0.
With the goals last night, 36-year-old AC Milan striker Oliver Giroud who has 115 caps, is now the oldest player to score for France at a World Cup.