France were relentless on the attack as they pushed for an opening goal but could not unlock a sturdy Poland until just before the break when Mbappe played a pin-point ball through to Giroud, who hammered it past a diving Wojciech Szczesny to claim his 52nd goal for Les Bleus.
Holders France continued to press after the break, with Giroud almost netting a second when he flicked Jules Kounde's cross just past the near post. But Mbappe did not miss in the 74th minute, unleashing a missile from just inside the penalty area that shot into the top corner.
Mbappe was not done, adding a second goal in stoppage time with another screamer to seal the win and take his total for the tournament to five.
Poland got a consolation goal from a Robert Lewandowski penalty.
France will next face the winners of the England versus Senegal game, being played later on Sunday.