France, who have once again moved ahead of Sweden in the standings, dominated the fixture from start to finish, but an impressive rearguard action from Luxembourg saw the visitors secure just their fifth point in the group.
The home side should have taken the lead in the 12th minute when Kylian Mbappe found Antoine Griezmann unmarked inside the Luxembourg box, but the Atletico Madrid attacker somehow lifted his effort over the crossbar.
Olivier Giroud, Mbappe and Djibril Sidibe also had half-chances in the 10-minute period that followed as the visitors struggled to contain a flowing French outfit, but somehow the score remained level in Toulouse.
Luxembourg had an opportunity of their own in the 21st minute after David Turpel broke into a wide position, but the lone forward missed the crossbar with a powerful effort, before Mbappe tested Jonathan Joubert down the other end moments later.
Paul Pogba was a fraction away from finding the top corner with a curling effort just past the 30-minute mark, before the Manchester United midfielder brought a fine save from 37-year-old goalkeeper Joubert in the 37th minute.
Griezmann smashed the crossbar with a dipping free kick five minutes before the interval as the match remained goalless, and that was how it stood at the end of a first period dominated by the home team.
France's frustrations continued in the opening 15 minutes of the second period, with Griezmann snatching at a couple of opportunities as Luxembourg, who were showing bits and pieces on the counter-attack, continued to hold Didier Deschamps's side.
Griezmann had a glancing header deflected behind 20 minutes from time, before Lacazette had one cleared off the line as the pressure increased in Toulouse.
Pogba saw a looping header land on the top of the crossbar in the 77th minute as France continued to throw players forward, but Luxembourg came close to a shock lead moments later when Gerson Rodrigues hit the post after a wonderful solo run.
Joubert again produced a smart save to keep out a low Sidibe effort in the 89th minute, and Luxembourg resisted the pressure in the final minutes to secure an incredible point against one of the fancied teams for the 2018 World Cup.