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Wendie Renard glanced in a header from a corner deep into injury time to consign Mark Sampson's side to a cruel defeat in Pennsylvania.
Marie-Laure Delie had headed France level with 10 minutes to go after Jordan Nobbs' 25-yard opening goal.
England's second game in the four-team tournament is against hosts the United States in New Jersey on Saturday.
They then finish with a game against Germany in Washington on 7 March.
Wednesday's result means England are still waiting for their first victory in the SheBelieves Cup, having drawn one and lost two in last year's event, and are without a win over the French since 1974.
Sampson's team are the lowest-ranked side in the event, with World Cup holders USA first, European and Olympic champions Germany second and France third.
The USA later beat Germany 1-0, with Lynn Williams scoring for the hosts.
Match ends, England 1, France 2.
Second Half ends, England 1, France 2.
Goal!  England 1, France 2. Wendie Renard (France) header from the centre of the box to the top left corner. Assisted by Amel Majri with a cross following a corner.
Corner,  France. Conceded by Demi Stokes.
Foul by Amandine Henry (France).
Jill Scott (England) wins a free kick in the defensive half.
Attempt missed. Wendie Renard (France) header from the centre of the box is just a bit too high. Assisted by Amel Majri with a cross following a corner.
Corner,  France. Conceded by Jill Scott.
Karen Bardsley (England) is shown the yellow card.
Foul by Amandine Henry (France).
Nikita Parris (England) wins a free kick in the defensive half.
Marie-Laure Delie (France) wins a free kick on the right wing.
Foul by Millie Bright (England).
Substitution, England. Isobel Christiansen replaces Jordan Nobbs.
Foul by Eugénie Le Sommer (France).
Lucy Bronze (England) wins a free kick in the defensive half.
Amel Majri (France) wins a free kick on the left wing.
Foul by Nikita Parris (England).
Substitution, France. Amel Majri replaces Griedge Mbock Bathy because of an injury.
Delay over. They are ready to continue.
Delay in match Griedge Mbock Bathy (France) because of an injury.
Sarah Bouhaddi (France) wins a free kick in the defensive half.
Foul by Ellen White (England).
Goal!  England 1, France 1. Marie-Laure Delie (France) header from very close range to the top left corner. Assisted by Élodie Thomis with a cross.
Marie-Laure Delie (France) wins a free kick in the attacking half.
Foul by Jade Moore (England).
Offside, France. Amandine Henry tries a through ball, but Wendie Renard is caught offside.
Eugénie Le Sommer (France) wins a free kick in the attacking half.
Foul by Lucy Bronze (England).
Substitution, France. Élodie Thomis replaces Gaëtane Thiney.
Hand ball by Eugénie Le Sommer (France).
Delay over. They are ready to continue.
Substitution, England. Alex Scott replaces Rachel Daly.
Substitution, England. Nikita Parris replaces Ellen White because of an injury.
Delay in match Ellen White (England) because of an injury.
Substitution, France. Eugénie Le Sommer replaces Kadidiatou Diani because of an injury.
Delay over. They are ready to continue.
Delay in match Kadidiatou Diani (France) because of an injury.
Amandine Henry (France) wins a free kick in the attacking half.
Foul by Ellen White (England).
England conceded a 95th-minute goal as they suffered an agonising defeat by France in their SheBelieves Cup opener.