Louis Bielle-Biarrey shone in a four-try display as Les Bleus finished on 21 points, two ahead of Ireland who beat third-placed Scotland 43-21 as England finished fifth, winning only one game in the Six Nations for the first time.
England played superbly against France, however, scoring tries through Tom Roebuck, Cadan Murley, Ollie Chessum (2), Alex Coles, Tommy Freeman and Marcus Smith.
Saturday's test, which marked the 120th anniversary of "Le Crunch", capped a remarkable championship, during which Italy beat England for the first time and Scotland came into the final day with a chance of winning their first Six Nations.
England rose to the occasion, but came up short despite scoring seven tries and more than 40 points on French soil for the first time.
The match got off to a pulsating start and remained frantic throughout, until Ramos' clinical penalty won it for France.
After discussions over where he would put down the tee for the championship-winning kick, Ramos slotted it over from 43 metres in the 83rd minute - a fitting end to a thrilling Six Nations.
Shortly after the start, Ramos chipped the ball through, finding Bielle-Biarrey in stride as the winger gathered the bouncing ball and sprinted over on France’s first incursion into the visitors’ half.
It was the 10th consecutive Six Nations match in which Bielle-Biarrey crossed the line.
NO CONTAINING BIELLE-BIARREY
England responded immediately, Roebuck finishing in the right corner after an eight-phase attack.
But there was no containing Bielle-Biarrey, who struck again when he scooped up Matthieu Jalibert’s deft kick to touch down for his second.
A series of missed tackles gifted England their second try as Theo Attissogbe failed to control Ben Spencer’s kick under pressure from Murley who dotted down.
Les Bleus stretched their lead with a Ramos penalty, yet England refused to take the easy points when awarded a penalty inside France’s 22.
Opting for the corner, they were rewarded as Ollie Chessum powered over after sustained pressure from the pack. Sensing vulnerability, England again kicked to the corner, and the gamble paid off as Coles crashed over to give the visitors the lead for the first time.
France regained momentum on the stroke of halftime with a penalty try after Ellis Genge collapsed a maul a metre from the line, earning a yellow card. With the extra man, the hosts struck again from the restart, Antoine Dupont releasing Bielle-Biarrey to complete his hat-trick.
Dupont then tapped a penalty and found Attissogbe on the right flank for the winger to score unopposed.
France gifted England another try just before Genge’s sin-bin time was over as Chessum intercepted a Jalibert pass to race to the line.
Marcus Smith, who had just come on for Elliot Daly, concluded a long possession spell for England with a try, landing the conversion to put England ahead again.
But France regained the lead when Bielle-Biarrey collected Dupont’s kick to score his ninth try of the campaign.
England centre Tommy Freeman tore through the French defence again to score and Marcus Smith converted to put the visitors ahead, but France were awarded a penalty after the clock had gone into the red and Ramos stepped up.
France have now won eight Six Nations titles, one more than England, and two more than Ireland and Wales.
