Coach Didier Deschamps was part of a France team that - needing just a point at home to qualify for the 1994 Finals - were stunned by Emil Kostadinov's 90th-minute victor that sent Bulgaria to the finals at Les Bleus' expense.
A win over Belarus on Tuesday evening would see them cement their spot at next year's World Cup in Russian Federation and give them a chance to repeat their 1998 heroics. Davy Propper, Captain Arjen Robben, and Memphis Depay scored for the Dutch as they beat Belarus 3-1.
Lacazette should have doubled France's lead just before the 30-minute mark after being found inside the Bulgarian box by Mbappe, but the Arsenal forward was denied by a brilliant challenge from Vasil Bozhikov.
The Swiss can qualify on Tuesday with at least a draw in Portugal, who needed Cristiano Ronaldo to come off the bench to rescue a 2-0 victory in Andorra. "When you have good players, it's normal to expect us to make a difference".
FC Copenhagen striker Pieros Sotiriou put Cyprus ahead early on as they looked for a win to maintain hopes of a play-off place, but two goals in three first-half minutes from Kostas Mitroglou and Alexandros Tziolis sent Greece two points clear of Bosnia.
The goal finally came in the 63rd minute when Ildefonso Lima could only get a slight touch to Joao Mario's cross, and the ball fell to Ronaldo to score.
Thomas Meunier had put Belgium in front after just four minutes, but goals from Haris Medunjanin on the half-hour and Edin Visca after 39 minutes put the hosts ahead going into the break.
"We did not have a great second period, and they were more aggressive".
In the other Group H afternoon kick-off, defender Joonas Tamm bagged a second-half hat-trick as Estonia trashed Gibraltar 6-0 at Estadio Algarve.
In Group H, Switzerland and Portugal set up a victor takes all meeting in Lisbon on Tuesday after both emerged victorious from their penultimate matches.