The former Montpellier forward scored his first Premier League goal against West Ham before the international break and then went on to grab a dramatic equaliser for France against reigning world and European champions, Spain.
The 26-year-old has revealed his delight at finally opening his account for the Gunners and says it has given his confidence a huge lift.
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“That and then setting up our second for [Theo] Walcott was important for my confidence. Hopefully this is where it all starts.
“But I was never worried that I would not score. As a striker, you know you will always have periods when you score less, times when the goals start to look smaller than normal."
Giroud also pointed out that it took Arsenal greats such as Thierry Henry and Bergkamp time to settle at the club but is hopeful he can achieve as much as the Dutchman who won three Premier League titles during his stay.
“There will always be periods of doubt for every attacker. It has happened before in my career, too," he added.
"But it took Henry nine games to score when he came to Arsenal, and Dennis Bergkamp seven, the same as me. If I can end up achieving as much as Bergkamp here, it will be OK.
“It is hard to stay confident, and it is hard to remember that you cannot just lose the quality that you needed to get you to where you are.
“You have to work hard mentally, to make sure you are playing with plenty of positivity. I have benefited from the support of lots of people in England: my team-mates, the fans, the coaches."