Goals in either half from Karim Benzema and Yoann Gourcuff, in a game that often took on the air of a training ground session, sealed a victory that now sees Les Bleus with nine points from their four games, with Belarus in second on eight after their 2-0 win over Albania.
Luxembourg's Metz-born goalkeeper Jonathan Joubert pulled off a cracking early save from a Philippe Mexes shot, scrabbling the ball around the post. But things turned bad for the visitors, ranked 130th in the world and habitual whipping boys in European qualifiers, from the subsequent corner in the 22nd minute as Gourcuff's cross found Benzema unmarked at the back post. The Real Madrid striker controlled the ball with his right foot as it looped over the stunned defence and drilled it home with a perfect left-footed volley.
Joubert was again on hand to gather an Abou Diaby shot as his defence held firm against a French attack that swamped the visitors in midfield. Gilles Bettemer had an opportunistic strike as the sole first-half showing for a Luxembourg side seemingly limited to a defensive gameplan.
Joubert rushed out to snaffle the ball from the feet of Guillame Hoarau in the 48th minute after the Paris St Germain striker rushed onto a Gourcuff through ball into the box. Things got worse for Luxembourg when captain Rene Peters received his marching orders after getting a second yellow card for a horrible two-footed lunge on Gourcuff.
The Lyon midfielder, at the heart of all of France's most productive spells, went close twice himself around the 65-minute mark, one shot soundly saved by Joubert and the other deflected as France sought a deserved second. France goalkeeper Hugo Lloris was finally called into action in the 74th minute, safely pocketing a Guy Blaise header.
But the home side's pressure finally paid off, man-of-the-match Gourcuff firing past Joubert's despairing lunge after a quickly-taken free-kick. Sami Nasri then made a hash of what should have been a third, blasting a Loic Remy cross high and wide from close range. And Gourcuff could only direct a late header from a pinpoint Payet cross directly at Joubert, who had the last word as he fended off a well-struck Nasri half-volley with his legs.