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Having been 3-1 up in the 80th minute against Switzerland, the world champions went on to concede twice late on before losing on penalties in a dramatic game in Bucharest.
Mbappe missed the crucial spot-kick in the shoot-out, while Pogba came in for criticism as despite his wonderful curling effort, he was at fault for Switzerland's equaliser when he was dispossessed in midfield.
Though there's no word of a mass fall-out amongst the squad, RMC Sport say it did get heated with the players' families in the stands and footage would suggest it was the case.
Rabiot's mum Veronique, who is also his agent, is said to have embarked on an incredible outburst where she called out Pogba for losing the ball for the third goal and told Mbappe's father to "reframe him and make him less arrogant".
As well as the verbal spat with Mbappe's dad, Veronique is believed to have also got into a "heated exchange" with Mbappe's mother, Fayza Lamari - while nearby journalists were also given a pasting.
All in all, Veronique reportedly spent around 20 minutes ranting and raving, with relatives of other France players believed to be "shocked" at the aggressive manner in which she behaved so soon after the loss.
Tensions appear to have been heightened from an argument earlier on between those close to Pogba and Rabiot's mother that was caused as a result of the former's reaction to errors the Juventus midfielder made.
Security stepped in to defuse the situation, asking Pogba's clan to calm down.
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