After straight-sets defeats for Kyle Edmund and Dan Evans on day one at Rouen's Kindarena, the chances of an away win were remote at best.
The doubles was much tighter and Murray and Inglot had chances to win each of the first three sets but instead suffered a narrow 7-6 (9/7) 5-7 7-5 7-5 defeat to end their campaign for another year. France now move through to a semi-final in September against either Serbia or Spain.
Doubles in Davis Cup rarely disappoints and this was another example of why the International Tennis Federation look certain to keep it at the heart of the weekend when changes to the competition are voted on in August.
Britain have twice come from 2-0 down to win Davis Cup ties, most recently against Russia in Coventry in 2013.
But, if that was unlikely, this was miracle territory - winning the doubles a formidable task even before considering Sunday's reverse singles.
Mahut was robbed of his Wimbledon-winning partner Pierre-Hugues Herbert through injury but Benneteau was hardly a weak substitute.
A grand slam winner himself in doubles and a player whose partnership with Mahut goes back to their junior days - they were US Open boys' champions in 1999.
The clay surface made things even tougher for Britain but Murray and Inglot, playing together for the fourth time, were the stronger pair for much of the match and were left to rue costly errors at important moments.
After 11 games dominated by the serve, they had three set points against Benneteau in the 12th game but could not take any of them.
Inglot, so impressive in the victory over Daniel Nestor and Vasek Pospisil of Canada in the first round in February, had started in the same vein.
But he netted a routine backhand on the third set point and then missed a straightforward volley as France fought back from 4-1 down in the tie-break to level at 4-4.
And, after a fourth British set point came and went, Benneteau forced the error from Inglot to give the French the advantage.
But the Londoner played a starring role in levelling the match, with his brilliant lob breaking the Benneteau serve at 5-5 in the second set before Murray served it out.
When the British team broke the Mahut serve to lead 3-2 in the third set, an 18th win from the last 20 Davis Cup doubles rubbers looked on the cards.
But, after seeing five break points in the set go begging, a missed Inglot volley on the sixth brought the French team back on terms.
A look of frustration from Murray told the story, with his partner impressive in so many ways yet still not quite at the level of the other players on the court.
It was an error from Murray that ultimately cost Britain the set, though, the Scot picking the worst moment for Britain's first double fault having saved two set points.
The pressure and atmosphere ramped up through the fourth set, reaching fever pitch when France forced a match point on the Murray serve at 5-6.
They could not take the first but a second followed and this time Murray's volley bounced off the tape and back onto his own side, sparking joyful French celebrations.
Read the original article on Eurosport: France knock Great Britain out of Davis Cup to make semi-finals