Antoine Griezmann, Raphael Varane and Olivier Giroud scored in the opening half and Kylian Mbappe struck late to put France top of the group ahead of Monday's home game against Iceland.
The Moldova fans erupted one minute from time when second-half substitute Vladimir Ambros got a consolation goal.
"The goal conceded does not take anything from our good game. It was a potentially tricky match but we di what we had to," said France coach Didier Deschamps.
In the other Group H matches, Iceland won 2-0 in Andorra thanks to Birkir Bjarnason and Vidar Kjartansson while Turkey beat Albania 2-0 through Burak Yilmaz and Hakan Calhanoglu.
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Kingsley Coman was meant to win his first France cap since November 2017 but he picked up a back injury in the warm-up and was replaced by Blaise Matuidi, who started on the left wing.
France got off to a slow start, but Paul Pogba flicked the ball over the Moldova defence and Griezmann volleyed the ball under the bar from point-blank range after 24 minutes.
Varane headed home from Griezmann's corner kick three minutes later as the home side started to become totally overwhelmed in their first meeting with France.
Giroud netted his 34th goal for Les Bleus with an angled volley from Blaise Matuidi's cross nine minutes from halftime, joining David Trezeguet in third place on the list of France's all-time top scorers.
Mbappe, who was having a frustrating night, netted from close range in the 87th to round off the victory.
France goalkeeper Hugo Lloris did not have a save to make until he was beaten by Ambros, who fired home with one minute left after some confusion in the French defence.
(Reporting by Julien Pretot; Editing by Ken Ferris)
