Air France said Air France Flight 65, from Los Angeles International Airport to Charles de Gaulle Airport in Paris, was diverted to Salt Lake City International Airport on Tuesday night local time.
Salt Lake airport officials said the plane had received a phone threat.
At about the same time a second flight, Air France 55, took off from Dulles International Airport outside Washington and was diverted to Halifax in Nova Scotia, Canada.
Passengers got off both planes safely and were taken to terminals. Authorities in both the US and Canada were preparing to search the planes with dogs, officials said.
The FBI was taking over the investigation of the plane in Salt Lake City, which was diverted because of a threat received by phone after take-off, Salt Lake airport spokeswoman Bianca Shreeve said.
In Halifax, the Royal Canadian Mounted Police was leading the investigation.
RCMP constable Mark Skinner said there were 262 people on board that plane, which also received an anonymous threat.