Wales did have their moments, though, particularly with the scoreline still at 1-0 midway through the second half, but they could not find the net and the hosts went on to see things through rather comfortably in the end.
With one eye on next summer's World Cup finals, Didier Deschamps named a strong-looking side that showed five changes from last time out, many of them enforced.
Backed by around 60,000 supporters in Paris, Les Blues were on top throughout the opening 45 minutes and will consider themselves unfortunate to have only taken a one-goal advantage into the break.
Blaise Matuidi and Corentin Tolisso both guided shots narrowly wide of the target to give Wales a little warning of what was about to come, while Griezmann saw his effort deflect off the legs of Wayne Hennessey and onto the crossbar.
The breakthrough goal did eventually arrive just short of a quarter of the way through, however, as Griezmann volleyed Tolisso's cross past Hennessey on the spin, with the ball somehow squirming under the Wales keeper.
The Euro 2016 runners-up, backed as second favourites for next summer's World Cup in Russia, really should have had a second when Kingsley Coman got away from out-of-position Ashley Williams down the right-hand side a few minutes after his side edged in front.
Coman's delivery was poor, though, picking out Hennessey's gloves at the front post rather than any of his four well-placed teammates alongside him.
Yet for all the home side's dominance, Wales had a glorious chance to level up the contest when Neil Taylor's delivery made its way all the way through to Chris Gunter, who tamely struck the ball straight at Steve Mandanda on cap number 84.
France looked to put the game to bed early in the second half, with Giroud testing Hennessey and Coman clipping the outside of the post with his attempt from slightly further back.
There remained just the one goal in it with a third of the game left to play, however, at which point Chris Coleman turned to exciting young trio Ben Woodburn, Ethan Ampadu and David Brooks, the latter two making their senior international bows.
Between them, they almost made a huge impact as Brooks pulled the ball back for Ampadu, whose shot deflected off Aaron Ramsey and was well kept out by Mandanda from just a few yards out.
The former Crystal Palace stopper was having to work far more in the second period, also standing strong to keep out Gunter's angled drive, while a third shot in quick succession was blocked in front of goal.
With gaps opening up at the back, Les Blues took full advantage as Giroud swept hope Kylian Mbappe's cutback - via a big deflection off James Chester - to effectively kill the game off with 19 minutes to play.
The final chance of the evening fell the way of Woodburn, who could only volley over the bar at full stretch after being spotted by lively fellow substitute Brooks.