Giroud's record-breaking goal came as Les Bleus defeated Poland 3-1 in the World Cup round of 16 stage on Sunday.
The 36-year-old has now scored 52 goals for France, moving one goal clear of Henry.
Giroud matched Henry's record after scoring twice against Australia in France's 4-1 win in their opening game.
Kylian Mbappe also scored a brace to help France seal progression to the quarterfinals.
"My wife and my children were there, plus my childhood friend. It's a childhood dream to beat Thierry Henry like that," Giroud told TF1 after the game.
"A lot of people told me it was coming, now I put it behind me and my obsession is to go as far as possible with the team.
"I was a little frustrated not to have been able to capitalise on one or two crosses that we made at the start of the match, so I really wanted to score this goal, just to stop talking about it!"
Defending champions France have now set up a quarterfinal meeting with England despite losing key players like Karim Benzema, Paul Pogba, Christopher Nkunku and N'golo Kante for the tournament.
"The adventure continues. We said to ourselves in the locker room that to live a magnificent experience together, we had to be united and be one," Giroud added.
"We were able to find the right words in the locker room, we have a great group of friends, it shows on the field. This team is rewarded for its efforts."
