Kurzawa has suffered a knee injury during training at Clairefontaine on Monday and, despite intensive treatment, has been unable to recover in time to face Bulgaria and Belarus in World Cup qualifying.
As a result, Didier Deschamps has turned to Amavi, who is on loan at Marseille from Aston Villa.
The 23-year-old is yet to play for Les Bleus at senior level, but was previously a regular at youth levels, including with the Under-21 side.
With Benjamin Mendy already injured, Deschamps' options at left back are now Barcelona's Lucas Digne and Amavi.
Laurent Koscielny, Paul Pogba and Ousmane Dembele are other key names ruled out of France's key double-header due to injury.