England were the red-hot favourite just five weeks after pipping France to the Six Nations title. They had 10 times the experience, and home advantage at Twickenham.
But a young France team of second and third stringers led for 65 minutes until the last minute of regulation time when England pulled out a converted try from a lineout drive to tie the score at 19-19.
That forced the final into 20 extra minutes of sudden death, with the first to score the winner.
England captain Owen Farrell had the first chance in the second minute, but his penalty kick from out front spun off the right post.
France tried setting up replacement flyhalf Louis Carbonel for a dropped goal but 12 phases in England’s half ended up with a penalty conceded.
In the second half of extra time, England's George Ford kicked into the left corner, France wing Alivereti Raka couldn't escape and Maro Itoje tied up the ruck to force a penalty.
After missing four penalties from seven goalkicks, Farrell lined up the penalty on the French 22 in from the left touch in the 96th minute and hit it straight through to crown England champion of the eight-team tournament that replaced the cancelled end-of-year tours.