Cunningham-South out of England's Six Nations finale with France
The Harlequins back-row suffered the injury after coming off the bench for the last quarter of England's dramatic 23-22 fourth-round win at home to reigning champions Ireland at Twickenham on Saturday.
England's Rugby Football Union said Sunday his place in the 36-strong squad that will begin preparations to face France in Lyon next Saturday would be taken by 20-year-old Newcastle flanker Guy Pepper.
Both centre Henry Slade and back-five forward Ollie Chessum remain available for a match against Les Bleus, who defeated Wales 45-24 in Cardiff on Sunday, after unspecified injuries suffered in ending Ireland's bid for consecutive Grand Slams.
Victory over Ireland has given England a chance of winning the Six Nations.
Ireland, however, will retain their title should they beat Scotland in Dublin before England kick-off on the Championship's concluding 'Super Saturday'.
