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 France 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.
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.
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.
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.
