Kylian Mbappe has scored four times in France's Euro 2024 qualifying campaign
The hosts were awarded a spot-kick after Konstantinos Mavropanos' awful challenge saw him kick the head of a jumping Antoine Griezmann.
Odysseas Vlachodimos saved Mbappe's first effort, but some Greek defenders had entered the penalty area with Mbappe scoring the second chance.
Mavropanos was later sent off for bringing down Randal Kolo Muani.
The victory means France have won all four of their qualifying matches and have not conceded. They are top of Group B and six points clear of Greece, who have played a game fewer.
Mavropanos' challenge on Griezmann left the striker bleeding, with the Atletico Madrid player needing a bandage around his head for the rest of the match.
There were 14 minutes of injury time played at the end of the second half, but Greece could not find an equaliser.
Elsewhere in Group B, Republic of Ireland gained their first points with a comfortable 3-0 home victory over Gibraltar.
-- Courtesy of BBC Sport