Thomas Tuchel has won the French Cup four times in the last four seasons, leading them to a 2-0 lead over 22 minutes with goals from Dani Alves and Neymar, only Presnel Kimpembe's goal before Mexes does not match the extra game.
Paris Saint Germain striker Kylian Mbappe has been omitted for two minutes before the end of the season, making him one of the biggest asset players in the penalty shoot-out.
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Christopher Nkunku missed his record in the Rennes win over their first league title since 1971, making PSG the only Ligue 1 side in the Champions League this season, 16 and the League Cup.
A week after returning for three months with an ankle injury, Brazilian striker Neymar had a serious threat to join the Copa America, but his team-mate Mbappe lost his feeling after the disappointing night at Stade de France.
Rennes, who left Lille and Olympique Lyonnais to the final, looked at different performances, after scoring the winner against Kimpembe.
"It's incredible, the fans have been waiting for a long time," said Rennes striker Mbaye Niang.
– Stade Rennais F.C. (@staderennais) April 28, 2019
"We have shown a character, it's worth it."
Tuchel has struggled to understand the loss.
"It's difficult to explain, we have not found any details, we have lost our focus," he told reporters at a press conference after PSG failed to win a trophy for the first time since 2012-13.
"It is a long time to be evaluated over the years, we need a few days to think about it."
PSG won the Champions League last season, following a two-point lead at Old Trafford after losing 5-1 to Lille on Sunday, hoping to win the Ligue 1 title.
GO & # 39; HOW IT WORKS
– Coupe de France (@coupedefrance) April 27, 2019
PSG began a good start when Alves shot a 20-yard shot in the 13th minute and Neymar scored two goals after Angel Di Maria.
But Rennes, the 11th Ligue 1, had only one goal for five minutes before being sent off when Kimpembe fired in a cross from Hamari Traore.
It was the first time PSG have conceded this season and 21 minutes into the second half of the match when Mexer headed Clement Grenier's goal.
PSG have missed several chances from Neymar and Mbappe, and Tuchel has made Julian Draxler a long time at Edinson Cavani.
Mbappe found a ball from Neymar, but his attempts to play football, resulting in a ban on Cavani, which was not the ideal place to put him on.
Mbappe was introduced on a red card directly to the knee in Damien Da Silva's knee.
He was in the dressing room when Nkunku equaled the spot-kick after his team-mates, including Neymar, replaced a penalty.