France reportedly name-dropped President Donald Trump during the process of the arrest. He was arraigned Monday at Sag Harbor Village Justice Court and released.
France was arrested at 7:30 p.m. Sunday and held overnight.
During the traffic stop, police determined France was operating his vehicle "in an intoxicated condition, Drake said".
They say officers saw indications France was intoxicated and found the pills during a subsequent search.
At this time, neither France nor NASCAR appear to have commented on the arrest.
TMZ reported that tests showed that France had more than twice the legal amount of alcohol in his bloodstream.
The president's relationship with the company goes back some years, to a proposed Trump Motor Speedway in Bridgeport, Connecticut.
France's grandfather Bill founded NASCAR in 1948, and his father ran the organization from 1972-2000. He stepped down as CEO so his son Bill France Jr. could take over.
France became chairman and CEO of NASCAR in 2003, a position that makes him one of the most powerful figures in sports.
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