Les Bleus took the lead after just 14 minutes when Djibril Sidibe slipped the ball through to Antoine Griezmann, who in turn played a neat one-two with Olivier Giroud before slotting the ball through the legs of Jasper Cillessen.
The Netherlands did not offer much of a threat against their opponents but nonetheless held on to head into the changing rooms just one goal down, despite being under the cosh for most of the first half.
This changed in the second half, however, as Kevin Strootman picked up two yellow cards in quick succession, the latter for a soft foul on Griezmann, to leave Holland down to 10 men 63 minutes in.
From then on, France succeeded in doubling their advantage as, 73 minutes in, AS Monaco forward Thomas Lemar drilled a volley from long range into the top corner.
Two minutes from time the hosts grabbed a third as Griezmann unselfishly laid the ball across for Lemar, who had the easy job of poking home into an empty net.
Dick Advocaat's humiliation was complete in the 91st minute when Mbappe played a one-two with Djibril Sidibe and swept home, leaving the Netherlands' qualification hopes in tatters.
The result means that the Euro 2016 hosts are on 16 points at the top of Group A, with Sweden second on 13 and Bulgaria third on 12.