With Eddie Jones' side having beaten Italy 34-5 in Rome earlier on Sunday (AEDT), Ireland went into the finale knowing it needed to at least win by seven points – or take a bonus-point victory – to claim its fifth Six Nations title.
After a combative first-half display Andy Farrell's side could not match its host after the interval, with a try and three penalties from the brilliant Romain Ntamack putting France in control by the 51st minute.
Ntamack's fellow half-back Antoine Dupont also put in a stellar display, opening the scoring six minutes in before turning provider for Ntamack's try.
Cian Healy had hit back for Ireland, but a penalty-try conceded by Caelan Doris gave France a lead it did not relinquish, and by failing to win by 31 points it handed England the title.
France struck first as Gael Fickou raced clear down the wing before finding Dupont, who easily got the better of Jacob Stockdale to slide in close to the sticks, with Ntamack adding the extras.
A frantic opening 10 minutes concluded with a lengthy TMO (television match official) check, which resulted in Anthony Bouthier receiving a yellow card for deliberately knocking the ball out of play.
Ireland made its numerical advantage count with a minute of Bouthier's time in the bin remaining, Healy forcing his way over to mark his 100th cap in style.
Sexton converted and then added a penalty to put Ireland ahead, but momentum swung France's way when Doris dragged back Francois Cros close to the line.
Another Sexton three-pointer dragged Ireland to within a point before Ntamack's penalty gave Les Bleus a 17-13 half-time lead.
Ntamack added five points to his tally three minutes after the restart, touching down after Dupont had superbly kept a France attack alive.
France's five-eighth missed the conversion but made no mistake with two penalties in the space of four minutes to nose Les Bleus 15 points clear.
Robbie Henshaw raced down Ireland's left to lunge over in the corner with 21 minutes remaining and provide hope for a comeback.
But Ntamack wriggled through a gap and set up Virimi Vakatawa to seal France's second-place finish, with Stockdale snatching a late consolation for the visitors.