Twickenham (United Kingdom) (AFP)
France, twice ahead by seven points and missing most of their first-choice players, were 19-12 up when England replacement forward Luke Cowan Dickie forced his way for a close-range try in the final minute of normal time.
England captain Farrell's conversion sent the match into two extra-time periods of 10 minutes each, with the side scoring first the winners.
Farrell, who saw a penalty hit the post two minutes into 'sudden death', then landed the winning penalty five minutes into the second half of extra-time.
Defeat was harsh on a game France side, who defied a vast gap in experience.
Their starting side, without the likes of scrum-half Antoine Dupont and back-row Gregory Alldritt, boasted just 68 caps between them compared to England's 772.
But France defied pre-game fears of a mismatch to lead 13-6 at the break after full-back Brice Dulin scored the only try of the first half.
France were the only team to have beaten Six Nations champions England this year, winning 24-17 in Paris in February.
But the French XV on Sunday bore little relation to that side, a release agreement with the Top 14 clubs limiting individual players' to three appearances on a team sheet in a six game end-of-year schedule re-arranged after the coronavirus pandemic.
But concerns that a novice France would be overwhelmed soon proved groundless in a match played in front of some 2,000 spectators -- the first time fans had been allowed into Twickenham since the Covid-19 pandemic.
Farrell kicked England into a 3-0 lead but France hit back in the 15th minute just as a chorus of 'Swing Low, Sweet Chariot', an England fans' anthem now regarded as controversial because of its associations with American slavery, rang round the ground.
England knocked on at a line-out, with France regathering the loose ball and working it across field.
Fly-half Matthieu Jalibert, 22, shrugged off the tackle of England hooker Jamie George, evaded centre Farrell and then delivered a superb delayed pass that sent full-back Dulin -- the most experienced player in the French XV with 30 caps -- in for a try at the left corner.
Jalibert converted and France led 7-3.
England full-back Elliot Daly, a long-range kick specialist, cut the lead to a point with a 48-metre penalty.
But France, playing at pace up front, created two more penalty chances for Jalibert, who landed both goal-kicks.
- Fallible Farrell -
On the stroke of half-time England declined a kickable penalty in the hope of scoring an equalising converted try from a close-range line-out.
But from an ensuing rolling maul, a succession of drives inches from the line failed to pierce the French defence before England prop Ellis Genge, who only replaced the injured Mako Vunipola on Saturday, knocked on as he tried to ground the ball.
Farrell reduced France's lead to 13-9 early in the second half with a 40-metre penalty
But the normally reliable goal-kicker missed his next two chances, both well within range, and France still led by four points heading into the final quarter.
With Jalibert off the field, replacement Louis Carbonel, just 21 and playing in only his second international, landed the 38-metre chance to put France 16-9 ahead with 10 minutes left.
Farrell's 73rd-minute penalty cut the deficit to four points.
But England gave Carbonel another chance and his successful penalty put France a converted try ahead at 19-12.
Cowan-Dickie then denied France in the 80th minute before England lock Maro Itoje produced a decisive turnover that led to Farrell's winning kick.
