France now play Germany aiming to settle old scores from past World Cups and Euros. And having home advantage and an attack led by Giroud and Antoine Griezmann that is starting to fire gives the French growing confidence.
The semi-finals will start on Wednesday however with Gareth Bale’s Wales taking on Cristiano Ronaldo and Portugal.
Giroud hit a goal in each half of the comprehensive victory at a rain-drenched Stade de France. He was joined on the scoresheet by Paul Pogba, Dimitri Payet and Griezmann. Atletico Madrid striker Griezman hit a brilliant chip on the stroke of half-time and now leads the tournament rankings with four goals.
French coach Didier Deschamps may have been worried however by the way Kolbeinn Sigthorsson and Birkir Bjarnason exposed France’s defensive frailties with two second-half goals.
Giroud was quick to pay tribute to Iceland, the revelation of the European Championship after their 2-1 victory over England.
“We scored five goals, we are very satisfied but Iceland never gave up. They fought with valour, they were very determined,” said the Arsenal striker.
“I want to pay tribute to them. They had a wonderful Euro,” added Giroud, who was brought off after his second goal to avoid getting a new yellow card that would have led to a suspension.
“I’m very proud. It’s been a fantastic tournament, something special for a small team like us,” said Iceland striker Gylfi Sigurdsson.
“We’ve probably overachieved. It is something no-one expected us to do, which is good because it gives kids back home hope that this is possible and hopefully in the future we’ll be back in the finals,” added the Swansea City star.
“We have problably 10-15 players who are at a really good age and we’ll be looking forward to the World Cup qualifiers which aren’t too far away.”
Iceland has only a population of 330,000 but Euro 2016 has put the country “on the map”, according to Arnor Ingvi Traustason.
“I’ve been getting messages from all over the world from people proud of us,” he said.
Didier Deschamps’ men will take on Germany in Marseille on Thursday for a place in the final.
Deschamps hailed his side’s performance though he acknowledged the weaknesses highlighted by the two goals.
“It’s not ideal even if I made some changes but there are so many positives to take from tonight,” he said.
“Germany are the best team, there is no doubt about that, even if Italy gave them a few scares. But we are there in the final four and we’ll give it our all,” said Deschamps.
Germany beat France in the 2014 World Cup quarter-finals. But France feel their defeat in the 1982 semi-final when Patrick Battiston suffered critical injuries even more.
Iceland, who had never beaten France in 11 attempts, kept faith with the side that shocked England, making European Championship history as the first team to name an unchanged line-up for their first five matches.
Sluggish starts have been a hallmark of France matches in the tournament, but the hosts quickly seized control and Iceland goalkeeper Hannes Halldorsson had to smother Payet’s early effort at the second attempt.
It took less than a quarter hour for France to make the breakthrough. Giroud raced onto Blaise Matuidi’s floated ball over the defence and drilled through Halldorsson’s legs.
Pogba headed home a Griezmann corner for his first goal of the tournament and in a powerful end to the half, Griezmann teed up Payet whose low drive whistled into the far corner.
Griezmann tucked away France’s fourth on the stroke of the interval, running onto Giroud’s pass and lifting the ball over Halldorsson.
Sigthorsson, who netted Iceland’s winner against England, scored for the second game running after poking in Sigurdsson’s cross on 56 minutes.
But France replied with Giroud beating Halldorsson to a Payet free-kick immediately before the Arsenal striker was withdrawn.
Iceland were rewarded for their perseverence though as they grabbed a second goal when Bjarnason headed in Ari Skulason’s cross on 84 minutes.
“Now we have gotten a taste of being at the big stage, we love it and we belong here,” said Halldorsson.