The problem for England, as Gareth Southgate acknowledged, is that if they insist on choosing elite opposition there is always the risk it will expose their own shortcomings. There were plenty of them here, the first time England have sieved three goals since a 4-2 defeat in Sweden in November 2012, and the cold, harsh reality for Southgate at the end of a punishing night is that it was a demoralising way to go into their summer break.

England should certainly feel distressed bearing in mind France had to play with 10 men after the moment, early in the second half, when Raphaël Varane brought down Dele Alli inside the penalty area and the video assistant referees confirmed it warranted a red card. Harry Kane’s penalty gave him his second goal, after he opened the scoring nine minutes into an eventful night, but France still managed to outdo their opponents in just about every department. England were fortunate not to suffer an even heavier defeat and it must have alarmed Southgate to see his team looking so vulnerable, particularly during the period of the match when they had an extra man.

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His players will have a better idea now why Kylian Mbappé is being touted for a possible world-record transfer. Paul Pogba, the man who currently holds that record, also reached the kind of heights that England will not encounter from opponents in their World Cup group. Yet the outstanding performer in Didier Deschamps’s team might actually have been the quick, elusive Ousmane Dembélé. France, to put it bluntly, were a cut above and there was something ironic about seeing a 4-4-2 team shimmering with this kind of menace while England experimented with 3-4-3, the de rigueur formation of modern football, and produced the same old flaws.

In fairness to Southgate, England’s shortcomings could not be pinned on the team’s new structure. More often than not, it was a question of players winning tackles, making clearances, remembering to mark their opponents and an old-fashioned tactic known as keeping the ball. Southgate had Phil Jones, John Stones and Gary Cahill in central defence but they all suffered against the speed and directness of Mbappé and Dembélé. Olivier Giroud also had a fine game and Southgate, a man who knows a thing or two about the art of central defence, seemed genuinely taken aback by his team’s second-half performance. For the first time as England manager, his voice was hoarse.

On a more positive note, Kane has now scored three times in two games for England and, factoring in his performances for Spurs, 10 in his last five appearances. Kane wore the captain’s armband again and showed again why, post-Rooney, Southgate intends to give him the captaincy on a full-time basis.

Ultimately, though, no team can defend this generously and expect to get away with it. Giroud also had a volleyed goal ruled out for offside and it was difficult to keep count of the number of times Mbappé was denied by either Tom Heaton or Jack Butland, England’s first- and second-half goalkeepers respectively.

Mbappé struck the crossbar with another shot and his speed on the break was a significant factor when it comes to England’s failure to take advantage after Varane’s dismissal.

As friendlies go, it had turned into an entertaining contest once Alli’s cross, followed by Raheem Sterling’s clever back-heel, left the overlapping Ryan Bertrand in a position to set up Kane for the opening goal. England had started well but once Les Bleus shook their heads clear of any early uncertainty they quickly must have realised their opponents were fragile at the back.

Samuel Umtiti made it 1-1 midway through the first half, turning in a follow-up shot after Giroud had headed a free-kick to Heaton’s right, and France’s second goal was a case of deja vu. Again, Heaton dived at full stretch to save, one-handed, and once more a France player was first to the loose ball. This time it was from Dembélé’s shot. The ball came back out and Djibril Sidibé fired in from eight yards.

Facebook Twitter Pinterest Harry Kane gets on the end of Ryan Bertrand’s cross to put England ahead at the Stade de France. He later added a penalty but England lost 3-2. Photograph: Michael Regan/The FA via Getty Images

If there was a criticism of Heaton, it was that on both occasions he turned the ball back into a dangerous area rather than pushing it further wide. The biggest problem for England, however, was the way they had defended to put Heaton in this position. Stones lost Dembélé before France’s second goal by diving into a challenge when he would have been better advised to stay on his feet.

Cahill was also partly to blame and Giroud, France’s target man, was not even marked before the first goal.

Strangely for a nation that prides itself on the physicality of its footballers, England also found it difficult to cope with the size and athleticism of their opponents. Southgate talked about his side looking tired in the last 20 minutes but that overlooked the fact he was entitled to make six substitutes and France had just come back from a World Cup qualifier in Sweden.

At 2-2, England ought to have been in a strong position to win in France for the first time since 1997. As it was, it was remarkable to see their lack of control and football intelligence against France’s 10 men. Eric Dier’s carelessness to give the ball away before the decisive goal was just another example. Pogba and Mbappé combined again, expertly moving the ball into Dembélé’s path, and his diagonal shot flew past Butland for the winner.