France 25-13 England
Fickou and Cros went under the sticks to give the hosts a commanding 18-6 lead at the break.
England threatened only briefly when Freddie Steward latched onto Joe Marchant's break to score after the restart, but captain Dupont made sure France would not be denied when he went under the posts and the hosts were seldom troubled in a comfortable end to the Six Nations finale.
The defeast marked a serious low point for Eddie Jones and his England players, who have serious ground to make up if they are to be considered genuine contenders for the Rugby World Cup in 2023.
France: Jaminet; Penaud, Fickou, Danty, Villiere; Ntamack, Dupont; Baille, Marchand, Atonio, Woki, Willemse, Cros, Jelonch, Alldritt.
Replacements : Ramos for Jaminet (76), Lucu for Dupont (76), Gros for Baille (49), Mauvaka for Marchand (49),Haouas for Atonio (54), Flament for Woki (71), Taofifenua for Willemse (49), Cretin for Cros (71).
England: Furbank; Steward, Marchant, Slade, Nowell; Smith, Youngs; Genge, George, Stuart, Itoje, Isiekwe, Lawes,Underhill, Simmonds.
Replacements : Ford for Furbank (76), Daly for Nowell (25), Randall for Youngs (64), Marler for Genge (64),Sinckler for Stuart (49), Chessum for Isiekwe (61), Dombrandt for Underhill (64).
Eddie Jones reacts to questions about his England future
Eddie Jones, when asked about his position as coach of England, told reporters: "That is not a question I need to answer. I just do my job. It's a question for other people.
"I'm disappointed for the fans and for the players. I obviously haven't done a good enough job, I accept that, but we're moving in the right direction.
"The results aren't good enough. When you rebuild a team it takes time."
France scrum-half and captain Antoine Dupont said: "This is our third tournament together as a team. We were very close twice so we know how difficult it is to win.
"We wanted to write our place in history.
"Of course we have next year's World Cup in mind, we discuss it between us, but for now we'll enjoy the Grand Slam and we'll start thinking about the World Cup later."
France team manager Raphael Ibanez, speaking to ITV: "Twelve years is a very, very long time and this was an intense final game but we have a fantastic group of players.
"We were thinking we needed to hold on and fair play to England, they tried to break us down."
Wales 21-22 Italy
The defending champions saw their Six Nations campaign end in a disappointing defeat as Italy racked up their only win of the tournament.
Wales were looking to celebrate a landmark day for captain Dan Biggar and veteran Alun Wyn Jones, with the former hitting the 100 caps mark, while Wyn Jones reached 150 appearances.
However, a huge upset occurred in Cardiff as an Italy side, winless in their last 36 Six Nations matches, put on a superb display.
The visitors started brightly, taking a 6-0 lead following penalties from Paolo Garbisi and Edoardo Padovani.
Wales answered back in a lethargic first half, but poor discipline allowed Italy to keep in contention through penalties.
With just minutes left on the clock, Italy secured the win with a try scored by Padovani following a dangerous break from full-back Ange Capuozzo.
Paolo Garbisi converted the try to spark wild scenes of Azzurri celebration in the Principality Stadium.
Wales coach reacts to loss
Welsh coach Wayne Pivac criticised his side's "unacceptable performance" after the full-time whistle.
"It's very disappointing. Lots has happened since last year, that's been well-documented.
"We came with a goal of giving ourselves an opportunity to finish third, which would have been a superb effort by the boys.
"After round one, we were building each week. But this was an unacceptable performance, which we must not let happen again.
"We had three good performances in this competition and two we weren't proud of. So it wasn't the complete competition. We'll get criticism from it - and rightly so."
Ireland 26-5 Scotland
Ireland kept the pressure on France towards the top of the table with a dominant display against a struggling Scotland side.
Dan Sheehan, Cian Healy, Josh Van Der Flier and Conor Murray scored the tries for the home side in the Aviva Stadium, with captain Johnny Sexton converting three of the four scores.
Gregor Townsend's side never truly looked as though they'd threaten during the match, with Pierre Schoeman's first half try a small consolation.
The defeat marked an 11th loss in 12 matches against Ireland, and ensured the hosts claimed the Triple Crown, ending an 18-year wait to win silverware on home soil.