But they now face a near impossible task, as Sweden thrashed Luxembourg 8-0 earlier on Saturday, with forward Marcus Berg scoring four goals, to extend their advantage over Dick Advocaat's men on goal difference to 12.
To have any chance of qualifying, the Dutch must beat Belarus and Sweden while vastly improving their goal difference.
Ahead of the clash with Bulgaria, the 1998 World Cup victor told the French media: 'Since the start, we know that this is a very important match for us.
'They are at home. "Along with that of PSG against Bayern (in the Champions League), it's the most important match".
"(I'm) not a saviour because there will be 11 of us on the pitch. "Well, you qualify to win it".
They have faced Bulgaria nine times away, managing just a single victory - in 1931 - with one draw and seven defeats. The Lions have only won one out of their last three games, most recently coming off a 3-1 defeat against the Netherlands.
France have injury issues as they are without Layvin Kurzawa, Laurent Koscielny, Benjamin Mendy, Ousmane Dembele and Pogba.
France face their final World Cup qualifying game against Belarus on Tuesday night, Didier Deschamps will hope to secure their place in Russian Federation next year.
In reality, however, the campaign has been far from simple; while Les Bleus sit one point clear at the top of the table, their place at Russian Federation next summer is not yet guaranteed.
Mbappe had the final chance of the first period after meeting a deflected free kick from Griezmann, but the Paris Saint-Germain attacker missed at the near post once again. "It gets me going, it's a source of huge pride to be able to rise to tougher and tougher challenges".