Didier Deschamps' side cruised to a 4-0 victory against their European rivals in the first Euro 2024 qualifier.
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In Koeman's first game back in charge of Holland, the Dutch found themselves 3-0 down at half-time as the French cut through with ease.
And they were three up after 21 minutes when Mbappe dashed through with searing pace as the ball found its way to his feet.
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With just Jasper Cillessen in his way, the Paris Saint-Germain star slotted past the goalkeeper in trademark fashion.
It marked his first appearance since being formally named as captain of the French national side.
Mbappe also grabbed an assist in the opening moments of the match, setting up Antoine Griezmann in the second minute.
Dayot Upamecano doubled the lead minutes later after some shoddy defending from a corner before Mbappe's strike.
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While Koeman's side enjoyed more than their fair share of possession, his second debut did not going to plan as Mbappe wrapped up the win in style with a stunning solo effort.
As for France, it's clear that they are not experiencing any form of a World Cup hangover having been beaten by Argentina in the final.
Mbappe scored a hat-trick in that match and has continued his fine form for the national side since.
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It is his 37th and 38th goal for the 2018 World Cup champions, which sees him overtake Karim Benzema for France goals.
Olivier Giroud is the record goalscorer for Les Bleus with 53 while Mbappe already has 67 caps at the age of 24.