France were twice denied by the woodwork and had 60 per cent possession and 18 attempts during an entertaining game as they slipped behind Italy into second place on head-to-head record in Group A1.
Zinedine Zidane was unimpressed with his side's defensive display after suffering his first defeat as France head coach against Italy on Thursday, but described the setback as "part of the process".
Les Bleus took an early lead at San Siro through Michael Olise to put one foot in the UEFA Nations League quarter-finals, but were pegged back by a Francesco Pio Esposito double and Davide Frattesi strike.
Italy seized control of the game in the second half after the two sides went in level at the break following an opening period dominated by Zidane's side.
Frattesi's goal arrived three minutes after Sebastiano Esposito had missed a penalty, and France conceded a second spot kick, converted by the younger Esposito brother, to take the game beyond the visitors.
"We started well and we were good in possession, but in the second half we ran into difficulties, especially defensively," Zidane told a press conference.
Asked if the team lacked courage, he replied: "No, quite the opposite.