It was a night to forget for Danish keeper Kasper Schmeichel, who let somehow contrived to let Giroud's tame shot squirm under his body in the fourth minute after a superb through ball from teenager Anthony Martial.
The 28-year-old was not helped by some non-existent defending two minutes later as Giroud was left unmarked to volley Lucas Digne's cross goalwards.
But once again Schmeichel spilled the ball and Giroud finished at the second attempt, looking almost embarrassed as he accepted the congratulations of his team mates.
Denmark's defensive difficulties were mirrored by their lack of firepower up front as, despite some good work by Nicklas Bendtner and Christian Eriksen, they did little to trouble the French rearguard.
Instead it was France who continued to create the better chances. Giroud almost completed his hat-trick in the second half but Schmeichel blocked the striker's attempted chip with his chest.
Martial also went close, nearly netting his first international goal for France when he clipped his half-volley narrowly over after chesting down Blaise Matuidi's pass with 10 minutes to go.
Erik Sviatchenko thundered home a late consolation goal for Denmark but France's Didier Deschamps will be the far happier of the two coaches, while Morten Olsen has plenty to ponder as his side heads for the Euro 2016 playoffs.
(Reporting by Philip O'Connor, editing by Mitch Phillips)
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