Henry was part of the France squad that won the 1998 World Cup on home soil at the age of 20, while Mbappe was only 19 when Les Bleus won the tournament in Russia in 2018.
Both are behind Giroud’s 137 appearances in France’s list of most capped players, with Henry ending his international career with 123 caps and Mbappe currently on 90.
France were aiming to defend their status as world champions at the 2022 World Cup in Qatar and duly reached the final.
Mbappe scored a hat-trick to take the final to penalties, only for his side to lose to Lionel Messi’s Argentina.
Mbappe is now well on track to surpass Giroud, who retired from international football last year following France’s defeat by Spain in the European Championship semi-finals.
“The record is getting closer, but it’s not something I think about,” Mbappe added. “I don’t know if it’s because I think I can beat it, or because I think there are more important things.
“Reaching this milestone so early is crazy, but I like it. I want to keep going and, above all, win games and titles.”
Against Ukraine, Bayern Munich’s Michael Olise gave Didier Deschamps’ side the lead after 10 minutes in their first match in Group D of qualifying for next year’s World Cup in the US, Mexico and Canada.
Paris St-Germain’s Ousmane Dembele replaced club team-mate Desire Doue at half-time but went off injured in the 81st minute and was replaced by Liverpool’s Hugo Ekitike, who came on for his debut.
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