Four goals in the first half helped France progress to their first semi-final in a major tournament since 2006 and they will now face world champions Germany in Marseille on Thursday.
“We are into the last week and I’m very happy about that,” said Didier Deschamps. “Germany are the best team. There is no doubt about that even if they had a few frights against Italy, who stopped them playing.
“But we are in the final four and we will go for it against the best team in the world.”
France will try to beat the world champions in a competitive game for the first time since the 1958 World Cup, although they beat them in a friendly last November on the night that Islamist militants struck in Paris.
France will be seeking revenge for World Cup semi-final losses in 1982 and 1986 and most recently a 1-0 quarter-final defeat at the 2014 World Cup in Brazil.
“We had the ambition to win and start the game well which we did. We were able to score a lot which was good for confidence,” said midfielder Dimitri Payet, who scored his third goal of the tournament.
“We now face the world champions and know what to expect. We need to rest and use what we learnt tonight.”
Man-of the-match Olivier Giroud hailed the team performance, but warned that they would still need to improve at the back against Germany.
Former France international David Ginola said this France team had perhaps finally shown its worth.
For Iceland the fairytale ended, but even after more than 80 minutes their fans, who have won so many friends since the tournament started, could still be heard backing their men.