In a court filing, FBI agents claim that Teresa Yuan sent threatening emails and videos to a website dedicated to the Oscar winner.
The messages, which were sent in July, included ramblings about wanting to play Russian Roulette with the actress.
In another video she says she would feel no regret "after it happens" because "that's apparently how it feels to be a killer."
On one recording, Yuan allegedly hisses and growls at the camera.
Cotillard won an Oscar for her role as Edith Piaf in "La Vie en Rose."
The Associated Press contributed to this report.