Martin O'Neill's men created all the chances of note during the opening 45 minutes, with Jeff Hendrick striking the crossbar, and Wes Hoolahan sent the travelling green hoards into raptures when he scored emphatically three minutes after the interval at the Stade de France.
Walters played a typically tireless hand to help Ireland into the ascendancy, despite feeling pain in his troublesome Achilles during the opening seconds of the Group E match.
The 32-year-old limped out of the action shortly before Zlatan Ibrahimovic's cutback was diverted into his own net by Ireland centre-back Ciaran Clark.
O'Neill told his post-match news conference Walters' predicament was "a concern" and the player will wait to see how his condition develops ahead of Saturday's match with Belgium.
"It's not great," he said. "I think I felt it after the first minute.
"Training was good the past couple of days but I didn't feel nowhere near 100 per cent after the first minute or so.
"I was struggling to sprint and jump. I got through the first half and a couple of runs in the second half but it just tightened right up.
"I think the right thing was to come off now let's see how it settles down."
Despite being forced to watch on as Ireland's advantage slipped away, Walters maintained there was plenty to enjoy in the team's performance.
"We're disappointed we conceded but I thought - first half especially - we played really well. I think we've got to take the positives," he said.
"We've got a point on the board and we go into the next two games with it all to play for.
"I thought the back four were exceptional, keeping one of the best players in the world [Ibrahimovic] at bay. All the midfield four were exceptional and for Wes to pop up with the goal, with his quality on the ball.
"I thought a great team performance from a lot of players. You've got to take the positives from the game.
"Three games, we're one in, we've got a point on the board. We've got to win one out of the two."