"I am sure a lot of you have seen the headlines. No excuses - I made a massive error of judgment and have let down my club, my fans and most importantly my family," Carter said on Facebook.
"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."
The All Blacks great was stopped in the French capital on the night of Wednesday, February 15, near the famous downtown Paris Street the Champs-Elysees, according to magazine closer.
They reported he had forgotten his driver's licence and his blood alcohol level was positive and measured at 0.98 grams of alcohol per litre of blood, nearly twice the limit of 0.5 grams.
The Racing 92 star had to leave his car, but was not placed in custody. Closer reported he would face a court appearance.
Leading French newspaper L'Equipe reported they had confirmed the incident as well.
Attempts to contact Carter in France failed.
And Carter's manager Dean Hegan didn't return Stuff calls on Friday, having earlier indicated to New Zealand media he was unaware of the alleged incident.
Carter, 34, was named World Rugby's player of the year following the 2015 World Cup final, a victory that brought an end to his celebrated 112-test career for the All Blacks. He remains the record points scorer in international rugby.
He went into the World Cup knowing it would be his last. In 2014 he signed a three-year deal for 2016-2018 with Racing 92, reportedly worth millions of dollars each season.
Carter has been sidelined for almost three weeks with a tear on his right adductor, limping out of Racing 92's loss to Lyon on January 28.
Reports in France suggest he may not be fit for action until the March 12 round 20 fixture against La Rochelle.
He has faced a difficult few months after being part of a doping inquiry into last year's French Top 14 final.
Carter and fellow All Black Joe Rokocoko were cleared of any wrongdoing by an investigation by French rugby.
On February 14, Carter and fellow former All Blacks star Ali Williams attended the Champions League football match in Paris, where Paris St-Germain upset Spanish giant FC Barcelona 4-0.
Photo: Henry Browne/ Reuters (Dan Carter has admitted to a "massive error", apologising for alleged drink driving in central Paris).