Teresa "Terri" Yuan, who lives in Queens in New York, was arrested by the FBI on Thursday in connection with the threats, Reuters reported. She was later released on $50,000 bail.
Yuan was accused of sending threatening videos and messages to Cotillard's fan site, sometimes more than 100 a day. The threats, which often sound incoherent, included references to playing Russian roulette with her.
"Would you be willing to play Russian roulette?" the message said. "If you weren't willing and you had no choice, I'd say "yeah, that's pretty unfair." But would you still like it that at least there's only one bullet in this pistol?"
In another video, she said she would feel no regret "after it happens" because "that's apparently how it feels to be a killer."
Yuan has been ordered to stay away from Miss Cotillard and warned her internet use will be monitored. Yuan's lawyer, Michael Schneider, declined to comment.
35-year old Cotillard lives with French actor Guillaume Canet and recently had a child.
She is one of France's most successful actresses and won an Academy Award, a British BAFTA and a French César in 2008 for her portrayal of Edith Piaf in La Vie en Rose, known as La Môme in France.
She also recently appeared in Woody Allen's recent film Midnight in Paris and has a role in the upcoming Batman sequel, The Dark Knight Rises.