France took the lead inside the opening three minutes, with Blaise Matuidi finding the top corner from an acute angle after Antoine Griezmann's deft touch set up a shooting chance for the Juventus midfielder.
France lost N'Golo Kante to a hamstring problem in the latter stages of the first period as Adrien Rabiot entered the field, and Bulgaria should have been level in the 36th minute when Hugo Lloris made a meal of a strike from Simeon Slavchev, but the Tottenham Hotspur goalkeeper somehow kept out a close-range header from Georgi Kostadinov.
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. The lead was doubled in the 86th minute by Andre Silva. The Dutch needed a victory in Barysaw to keep alive any hopes of a top-two finish, but despite a third goal in two games from Brighton and Hove Albion midfielder Davy Propper, Belarus equalised through Maksim Volodjko. However, the latter have the superior goal difference and they may add to that against a side who have lost all of their nine game so far.
Meanwhile, Portugal struggled against Andorra at the Estadio Nacional in Andorra La Vella. "When you have good players, it's normal to expect us to make a difference".
Greece could also finish second in the group as they trail Bosnia-Herzegovina by a point ahead of their trip to Cyprus.More news: Five toddlers burned alive in arson attack on nursery
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The 1998 world champions lead Sweden by one point in Group A with two matches to play, but France need little reminding of the pain inflicted upon them by the Bulgarians in one of the national team's darkest hours.
They were more aggressive.
The visitors continued to dominate and almost found a second seven minutes later when N'golo Kanté found Mbappé in space on the left and the PSG forward forced a fine save from Plamen Iliev at the near post.
Edin Visca then completed the comeback for Bosnia before half-time after an error from Jan Vertonghen, but Chelsea striker Michy Batshuayi hit back to equalise in the second half and Vertonghen put Belgium ahead again.
The other early kickoff in that group saw qualifying rookies Gibraltar suffer yet another thrashing, loosing 6-0 at home to Estonia.