Didier Deschamps took no chances against a side ranked 170 in the world, starting the likes of Kylian Mbappe, Antoine Griezmann and Paul Pogba, and France had the three points secured with three goals in the opening 36 minutes.
Griezmann volleyed in the first after a clever one-two with Pogba before Raphael Varane headed home from a corner. Olivier Giroud then turned in Blaise Matuidi's cross for his 34th French goal, moving him level with David Trezeguet in third in the country's all-time top scorers.
Mbappe then added a fourth with a sharp first-time finish late on to complete a comfortable night for the reigning World Cup holders, whose clean sheet was ruined by substitute Vladimir Ambros scoring an 89th-minute consolation.
34 – With 34 goals, Olivier Giroud has become the 3rd joint-top goalscorers in France national team’s history (level with David Trezeguet). Podium. pic.twitter.com/M2Ko3HHAcY— OptaJean (@OptaJean) March 22, 2019
For the first 24 minutes, France barely had a sniff of goal, but 12 minutes later they had put the put the game to bed with three goals in swift succession.
The first was the pick of the bunch, Griezmann rolling the ball into Pogba and continuing his run to get on the end of the Manchester United midfielder's chipped pass, the Atletico Madrid forward then firing an unstoppable volley into the net.
Oleg Reabciuk almost handed the world champions a second when he volleyed Layvin Kurzawa's cross just wide of his own goal, but from the resulting corner France scored anyway as Varane's header from Griezmann's near-post corner could not be stopped by defender Ion Jardan at the back post.
Mbappe's weak finish prevented Griezmann from claiming a second assist, though France were soon 3-0 up as an unmarked Giroud got a faint touch on Matuidi's cross with a volley.
While Deschamps' side took their foot off the accelerator after the break, Pogba was still twice denied by Alexei Koselev, the second save a brilliant one-handed stop to a header from Griezmann's free-kick.
Mbappe eventually got in on the act three minutes from time, profiting after good pressure from substitute Thomas Lemar. It was not the final goal of the game as Ambros pounced when the ball came back off a post from Vitalie Damascan's header.
Referee Aleksandar Stavrev then correctly booked Mbappe for diving to try and win a penalty as Koselev rushed out in stoppage time.
What does it mean? France handle business, but sterner tests lie in wait
Moldova are the lowest-ranked nation in Group H so little can be gleaned from France's comprehensive victory. The visit of Iceland on Monday will be a tougher assignment, while Les Bleus' group also includes Turkey and Albania.
Griezmann shines with goal and assist
France were awoken from their early slumber by Griezmann's emphatic finish, and it was from his corner that Varane added the second. Had Mbappe been sharper and Koselev not thwarted Pogba, Griezmann might have ended with a hat-trick of assists.
Mbappe not at his marvellous best
Fans at the Stadionul Zimbru would arguably have been most excited about witnessing Paris Saint-Germain forward Mbappe up close, though he was overshadowed by the other attackers in white shirts. Even after his goal, his night was still soured by a terrible dive that he was rightly booked for.
France face Iceland in Paris on Monday, five months on from their last meeting, which ended in a 2-2 draw as Deschamps' side scored twice late on. Moldova visit Turkey on the same night.