Les Bleus dominated, with Kylian Mbappe having an early goal dominated out for offside and Aurelien Tchouameni’s bicycle kick being tipped onto the bar.
Giroud set up Mbappe for a fantastic opener, taking on a number of defenders before firing in from 16 yards.
AC Milan striker Giroud, 35, brilliantly headed in France’s second.
At 35 years and 357 days, he’s 70 days older than Roger Marche was when he scored against Spain in December 1959.
Giroud is now solely two goals behind Thierry Henry’s France record of 51.
France, who would have been relegated if they’d lost, transfer above Austria going into Sunday’s Group A1 finale in Denmark.
Croatia lead the group following a 2-1 win against Denmark, who would have sealed top spot themselves had they received in Zagreb.
Defender Borna Sosa put the hosts forward together with his first worldwide goal. Manchester United midfielder Christian Eriksen levelled with a sensational long-range strike, however two minutes later Lovro Majer scored the winner from exterior the field.
Croatia simply want to beat Austria on Sunday to qualify for subsequent year’s finals and e book a Euro 2024 play-off place.