Both flights landed safely Tuesday night, and were searched and given the all-clear by Canadian and U.S. authorities.
Flight 65, en route from Los Angeles to Paris, was diverted to Salt Lake City after a bomb threat was called in from the ground, a U.S. government official said.
The official did not know whether anyone was arrested and was not aware of any unruly passengers on board.
Shortly afterward, Air France Flight 55 from Washington's Dulles International Airport to Charles de Gaulle Airport in Paris was diverted to an airport in Halifax, Nova Scotia -- also because of a called-in bomb threat, a government source said.
The source did not know whether the same person called in both threats.
No U.S. military aircraft were scrambled in either incident, NORAD spokesman Preston Schlachter said.
"Diversion of flights are the most draconian response to a bomb threat," CNN national security analyst Juliette Kayyem said.
Passengers questioned by FBI
YouTube sensation Trevor Moran was on Flight 65, headed from Los Angeles to Paris to shoot a music video.
He said the pilot told passengers the plane had to make an emergency landing.
"There were huge buses when we landed that they loaded us all on," he told CNN.
"Everyone on the flight is waiting in this lobby. Nobody knows what's going on."
Keith Rosso, who was on the same flight, said he had just finished dinner when the staff abruptly took trays away and said the plane was landing because of "unsafe flying conditions."
'This is terrorism'
Even though the flights landed safely, CNN law enforcement analyst Jonathan Gilliam said there are reasons for serious concern.
"One thing that has to be clear is that we may call this a hoax, but the reality is, terrorism -- which we see going on in France right now, and here -- is a tactic used to affect a psychological or political change on a community. And that is what this is," Gilliam said.
"It may be a hoax, as far as a bomb threat. But this is terrorism."
The bomb threats on Paris-bound flights came four days after a wave of deadly attacks terrorized the French capital.
At least 129 people were killed in an onslaught of bombings and shootings Friday night
. French President Francois Hollande declared a state of emergency.
The terror group ISIS claimed responsibility. Afterward, French warplanes have launched waves of airstrikes on ISIS' de facto capital of Raqqa, in northern Syria.
The Air France threats aren't the only bomb scares since the Paris attacks.
"Serious plans for explosions" forced the evacuation of a stadium in Hannover, Germany
, on Tuesday night before a Netherlands-Germany soccer match, a local police chief told Germany's public broadcaster NDR.
Two tips forced officials to cancel the match about 90 minutes before kickoff.
No explosives were found at the stadium.