After Paul Pogba had opened the scoring, the Arsenal ace produced a sublime lobbed finish before striking again with a looping header following Loic Remy's strike
Six minutes after half-time the forward controlled Mathieu Valbuena's pass on the edge of the box and struck a volley high into the net for his sixth international goal, as the hosts thumped their ragged opponents in the Stade de France on Tuesday.
Didier Deschamps' men were already one to the good at that point, Paul Pogba having headed in Valbuena's pinpoint cross on 15 minutes as the home side made a bright start to proceedings.
Loic Remy, on as a substitute for Antoine Griezmann, scored just after coming on in the 67th minute after being played through by a glorious first-time pass from Mathieu Debuchy.
Giroud added his second and France's fourth two minutes later, adjusting his body to head home after another assist from Valbuena, as the first of France's three pre-tournament friendlies ended in comfortable victory.
Deschamps will have been pleased with his side's attacking prowess, with the impressive Valbuena especially dangerous in creating three of the four goals as the French look to put the nightmare of their World Cup campaign in South Africa four years ago behind them.
The hosts made a blistering start, twice bringing flying stops out of Norway goalkeeper Orjan Nyland in the opening two minutes.
Nyland first tipped Griezmann's glancing header over the crossbar and then kept out Giroud's powerful nodded effort from Valbuena's resulting corner.
Griezmann went close again in the 10th minute, flicking Yohan Cabaye's miscued volley narrowly wide.
France's early dominance paid off five minutes later, when Pogba glanced in Valbuena's left-wing cross, although the Marseille man looked to have received the ball in an offside position before delivering.
Pogba almost doubled his and France's tally in the 19th minute, fizzing a low effort just wide of the right-hand post after driving into space on the edge of the box.
After weathering the early storm the visitors grew into the game, Havard Nordtveit sending a 25-yard free kick wide of the post before Alex Tettey tested Stephane Ruffier with a low shot from a similar distance.
Tom Hogli then linked up with Joshua King down the left and stung the palms of Ruffier from a tight angle in the 42nd minute as Norway ended the half on top.
France began the second period as they had the first and extended their advantage with a moment of real quality.
Valbuena played the role of creator once more, picking out Giroud on the edge of the box, and the Arsenal man took a touch to control before looping a fine volley over Nyland into the top right-hand corner.
Remy, fresh on as a replacement for Griezmann, made it three by slotting past Nyland following Debuchy's perfect pass, before Giroud's flicked header compounded Norway's misery.