The referee Nicola Rizzoli pointed to the spot. Robbie Brady sent Hugo Lloris the wrong way and the ball went in off the inside of the right hand post.
To the consternation of the partisan crowd at the Stade de Lyon, the hosts were unable to respond immediately and they were booed off at half-time.
A brighter, more direct team emerged in the second-half. Deschamps replaced N’Golo Kanté’s sagacity with Kingsley Coman’s dynamism. The tactical shift amplified the pressure on Ireland’s defence.
The rearguard cracked in the 57th minute. Bacary Sagna whipped in a cross from the right and Antoine Griezmann rose to head past Darren Randolph. Four minutes later, France had the ascendance. Griezmann latched onto Olivier Giroud’s knock down and he slotted past the exposed Randolph.
Ireland’s difficulties were magnified after 67 minutes when Shane Duffy chopped down Griezmann just outside the box. Rizzoli handed him a straight red card and with it, all Irish hopes were effectively extinguished.
“We didn’t help ourselves by conceding the penalty so early,” said Deschamps after the game. “You have to be so careful. Many people had anointed Croatia as the champions and they went out on Saturday night.
"It was hard for us too, but mission accomplished," he said. "You shouldn't be too calculated. The players need discipline but sometimes we're better when we go a bit crazy. We really speeded things up and that's when we are most dangerous."
France will play at the Stade de France on 3 July against England or Iceland who play on Monday night in Nice.