Substitute Fickou was let loose on the left wing and scored with three minutes left, denying England a comeback victory after they had battled back from a 13-point deficit.
France, desperate to erase memories of last year's championship when they managed only one victory, stunned England when winger Yoann Huget touched down for the first try after 30 seconds.
Huget increased the French advantage with a second try 10 minutes later before three points from Owen Farrell's boot and a Mike Brown score five minutes before halftime gave England hope.
A brilliant Billy Vunipola continued to inflict bruises on the French defense early in the second half and England deservedly nosed ahead when he set up debutant Luther Burrell for the visitors second try.
Danny Care's drop goal made it 21-16 before a Maxime Machenaud penalty and one from Alex Goode left England five points ahead.
But France were not done with and the late replacements paid off when hooker Dimitri Szarzerwski timed his pass to perfection to allow Fickou to cross and Machenaud to kick the winning points.