Giroud was celebrating his 35th birthday on Thursday but he did not mark the occasion with a recall to coach Didier Deschamps' squad, having already been dropped for a series of World Cup qualifiers at the start of September.
The AC Milan striker, who sits just five goals away from equalling Thierry Henry's all-time record tally of 51 for Les Bleus, also recently tested positive for Covid-19.
Kante, like Giroud a key part of the France team that won the World Cup in Russia in 2018, is ruled out after his club Chelsea revealed earlier this week that he had contracted Covid-19.
France play Belgium in Turin next Thursday, October 7, in the semi-finals of the Nations League, with hosts Italy taking on Spain the previous day in Milan.
The winners will meet in the final at San Siro on Sunday, October 10 for the right to succeed Portugal, who won the inaugural Nations League in 2019.
Kingsley Coman has also been left out of the France squad after recently undergoing heart surgery, while there is no place for veteran Marseille goalkeeper Steve Mandanda, the long-time back-up to Hugo Lloris.
Among the players coming back into the squad are Bayern Munich pair Benjamin Pavard and Lucas Hernandez, Monaco striker Wissam Ben Yedder and Juventus midfielder Adrien Rabiot.
There is also a place for uncapped 22-year-old midfielder Matteo Guendouzi, who is currently on loan at Marseille from Arsenal.
France squad for UEFA Nations League finals:
Goalkeepers: Benoit Costil (Bordeaux), Hugo Lloris (Tottenham Hotspur/ENG), Mike Maignan (AC Milan/ITA)
Defenders: Lucas Digne (Everton/ENG), Leo Dubois (Lyon), Lucas Hernandez (Bayern Munich/GER), Presnel Kimpembe (Paris Saint-Germain), Jules Kounde (Sevilla/ESP), Benjamin Pavard, Dayot Upamecano (both Bayern Munich/GER), Rapahel Varane (Manchester United/ENG).
Midfielders: Matteo Guendouzi (Marseille), Theo Hernandez (AC Milan/ITA), Paul Pogba (Manchester United/ENG), Adrien Rabiot (Juventus/ITA), Aurelien Tchouameni (Monaco), Jordan Veretout (Roma/ITA).
Forwards: Wissam Ben Yedder (Monaco), Karim Benzema (Real Madrid/ESP), Moussa Diaby (Bayer Leverkusen/GER), Antoine Griezmann (Atletico Madrid/ESP), Anthony Martial (Manchester United/ENG), Kylian Mbappe (Paris Saint-Germain).