France were 3-0 up midway through the second period thanks to powerplay goals from Laurent Meunier and Damien Fleury while Pierre-Edouard Bellemare scored on a delayed penalty call in between.
However Britain came out fighting in the third and final period in Latvia and pulled two goals back on France thanks to Ben O'Connor and birthday boy Robert Lachowicz.
But it wasn't to be for Britain, who opened the final Olympic qualifying tournament with a 6-2 defeat to hosts Latvia, as Charles Bertrand netted France's fourth shortly after as it ended 4-2.
With Latvia and Kazakhstan both victorious in their first games, the latter beat France 3-2, and due to face each other next Britain now cannot win the tournament, the requirement to qualify.
Danny Meyers was called for hooking 23 seconds in before Ashley Tait followed suit for slashing in the ninth minute to give France their second powerplay.
And, having failed to score on the first, France didn't miss out second time around as Meunier unleashed a big shot from the right past Stevie Lyle.
Britain recovered though and had a great opportunity when Jason Hewitt was found in front of goal however Fabrice Lhenry was on hand to deny him from close range.
Lachowicz created an opening at the beginning of the second period before Damian Raux rung the post and France scored their second seven minutes in.
With a delayed penalty called and France's goalie pulled to create an advantage, Bellemare fired home with Sacha Treille and Yohann Auvitu credited with the assists.
However there was an element of controversy in the goal with Mark Garside appearing to have touched the puck beforehand, which would stopped play immediately and seen the penalty given.
France made it 3-0 five minutes before the end of the period as, with Colin Shields penalised for slashing, Fleury combined with Baptiste Amar to score.
However Britain responded immediately in the third period and, on the powerplay themselves after Johann Morant was called for hooking, O'Connor scored.
Robert Dowd got on the end of a shot from the blue line with the puck working its way past the outstretched Lhenry and into the path of O'Connor who tucked home.
And the comeback continued just over seven minutes later Lachowicz scored his first goal for Britain however Bertrand capitalised on a Lyle mistake behind the goal to end it shortly after.
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