The three-times World Player of the Year, who plays in France's Top League for the Racing club, was tested by police after being stopped in his car near the Champs Elysses in the centre of the city, reports said.
"I am sure a lot of you have seen the headlines," the 34-year-old World Cup winner wrote in a message on his official Facebook page (@dancarterallblack).
"No excuses - I made a massive error of judgment and have let down my club, my fans and most importantly my family.
"I will have to now let the police/court process run its course and face the consequences. I am just glad no one was harmed. Sorry."
No one was immediately available for comment at Carter's management agency in Auckland on Friday.
Carter tweeted a picture of himself at the Champions League soccer match between Paris St Germain and Barcelona at the Parc des Princes on Wednesday evening.
Punishments for drink-driving in France range from an on-the-spot fine to two years in prison.
(Reporting by Nick Mulvenney; Editing by Ken Ferris)
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