Carlos was already on a yellow heading into injury time, with PSG 1-0 up thanks to Angel Di Maria's 12th-minute strike.
But the 24-year-old accidentally tripped up the match official as the latter cut across him during a PSG counter-attack.
Chapron was fuming, and swung a leg out at the Brazilian defender after he hit the deck. He then flexed his powers by showing Carlos a second yellow card.
Nantes man Carlos was incensed and had to be held back by his team-mates before eventually trudging off the field in a huff.
"I received 20 SMS from all over the world telling me that this referee is a joke," Nantes president Waldemar Kita told L'Equipe post-match.
"What do you want me to say to you? If I talk too much, I will be summoned by an ethics commission. We have no right to say anything.
"It's still scandalous to see that. We give a red card to a player who did nothing. Where are we? He has to go back to school.
"Chapron has to rest and get a massage, it works like that now, we cannot see him. I'm waiting for the green light, otherwise I'll be killed. It's amateurism."
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