Paris St-Germain forward Randal Kolo Muani fired into the roof of the net to give France the lead in Athens.
But Anastasios Bakasetas equalised for Greece with a 20-yard volley, before Fotis Ioannidis guided home a cross.
That forced boss Didier Deschamps to turn to his bench, with Kylian Mbappe coming on to set Youssouf Fofana up for their equaliser with 16 minutes left.
The visitors, who had already qualified, thought they had found a late winner when Kingsley Coman’s deflected cross span towards goal but the referee and video assistant referee decided the ball had not crossed the line.
France, who had only conceded one goal in their first seven qualifying games, finish top of Group B while Greece, who are seeking a place at the European Championship finals for the first time since 2012, will face Kazakhstan in the play-offs on 21 March.
Should they win that game the 2004 champions will then face Georgia or Luxembourg on 26 March for a place in the finals.
Elsewhere in Group B, the Netherlands, who finished second, thrashed Gibraltar 6-0, with Liverpool forward Cody Gakpo rounding off the scoring.
The 24-year-old scored four minutes after coming off the bench as his left-wing cross drifted into the far corner.
Feyenoord’s Calvin Stengs scored his first international goals on the way to a hat-trick, while Mats Wieffer and Teun Koopmeiners were also on the scoresheet.
France and the Dutch will find out who they face in the group stages in Germany when the draw takes place on 2 December.
Source : BBC