Giroud, 25, set to face Southampton today, was also jeered by French fans when he was subbed in the 2-0 win over Belarus on Tuesday.
He said: "In reality, the pressure doesn't come from following in the footsteps of Henry, Pires, Petit or Vieira but Robin van Persie's departure.
"I was expecting to be his substitute but now I'm his natural successor. If I do have pressure, it's on that level.
"Yet I'm not the type to panic. But it's true you must realise what French players represent at this club, it's down to me to keep that tradition going.
"The coach has faith in French players and signs a lot of them. The coach's French touch is what gives the club its charm.
"Wenger's the person I will learn a lot from, because I still need to improve. I know it and he knows it.
"He told me I'd made the right choice coming here, to improve."