PSG teenager Mbappe was one of the stars of Les Bleus' march to glory in Russia and he dazzled during the opening stages of a first game back at the Stade de France for Didier Deschamps' side.
There was a sense of inevitability to his 14th-minute opener but Ronald Koeman's men were rewarded for their persistence with Ryan Babel's equaliser after the hour mark.
Chelsea striker Giroud failed to score at Russia 2018 but was on hand to volley home substitute Benjamin Mendy's cross for his first France goal in 11 matches.
Mbappe drew two early saves from Jasper Cillessen before becoming the beneficiary of some dreadful Netherlands defending.
A couple of botched clearances from Babel and Daley Blind were compounded when Quincy Promes headed into Blaise Matuidi's path, leaving Mbappe to tap in the Juventus midfielder's low cross.
By the time the hour passed, France had allowed a position of strength to drift and did not heed the warning of Georginio Wijnaldum bustling into the box to drag wastefully wide.
Kenny Tete charged into space down the right, beyond the recently introduced Mendy, and the on-rushing Babel dispatched his fine delivery at the near post.
Memphis Depay then lashed into the side netting, with the Lyon star wasting another promising position in the 71st minute.
France's response was decisive, although the previously impressive Cillessen will be disappointed to have palmed Giroud's left-footed effort into the net.
What it means: World champions set the pace
Following France's opening 0-0 draw with Germany in Munich on Thursday, they are out in front in Group A1 of UEFA's inaugural in-season competition, while Netherlands must try to get off the mark next month.
