Didier Deschamps admitted France had needed to dig deep after taking another step towards Euro 2020 with a hard-fought win in Iceland.
Chelsea striker Olivier Giroud scored the only goal of the Group H qualifier in Reykjavik from the penalty spot after 66 minutes.
The 1-0 victory means the world champions can secure their place at next year’s tournament by beating group leaders Turkey on Monday.
Similarly, Turkey could also qualify with a victory, and the losers would have to wait another month to try again, so there is plenty riding on the clash at the Stade de France.
Deschamps told TF1: “We needed to win here and that wasn’t simple even if we had several chances to score a second goal. They’re always dangerous from set-pieces.
“That game was all about commitment and we lived up to that. We had a lot of the ball and we could have been out of danger with the chances we had at the end of the game.
“It’s a good win ahead of Monday, an important step.”
Forward Antoine Griezmann, who was fouled for the decisive penalty, said: “It was very difficult, a really hard match.
“We needed to take the three points and now we have an important game coming up at home. We’re going to suffer against Turkey and we’ll need to prepare well for it.”
For Iceland, the result left them six points adrift of the group leaders with three games to play.
Coach Erik Hamren, the former Sweden boss, told reporters: “I’m proud of the players and the team. We did everything we could, but of course I am disappointed not to get the result.
“Proud but frustrated – that’s how I feel right now.”