This time, though, Draper made it on to court, appearing initially nervous – but without the compression sleeve that supported him through recent appearances.
He was smiling by the third game, when he read a tricky Atmane serve well and pulled off an unlikely winner to delight the crowd and level the score to deuce.
Having failed to break Atmane as the Frenchman won the first set 6-3, Draper began to show glimpses of the glittering 2025 form which earned his number four ranking last June.
In the second set, the Montreal crowd whooped as Draper executed a powerful cross-court forehand on course to a dominant 6-2 set win.
He looked primed for a comeback victory but a different, depleted Draper returned for the third set, surrendering the opening game having led 40-15.
The 2024 US Open semi-finalist appeared frustrated in the fourth game when he passed up a gift of a break point, firing a tired forehand into the net.
After he was broken for 4-1 in the next, Draper sat down during a change of ends and was overcome with emotion, wiping tears from his eyes.
Atmane served out to claim the match and will face Russian Karen Khachanov in the second round.
Draper has a wildcard entry to the Cincinnati Open, which starts next week, but the incident puts his involvement in doubt, and that of the US Open which begins on 23 August.
Earlier, British number five Jacob Fearnley beat France’s Adrian Mannarino 7-6 6-4 to set up a second-round tie against the Czech Republic’s Jakub Mensik.