The double-decker aircraft carrying 496 passengers and 24 crew had taken off from Paris on Saturday bound for Los Angeles and was several hours into the flight when the blow-out occurred.
Passengers recounted hearing a loud bang followed by violent shaking, with video and photos posted on social media showing extensive damage to the outer starboard engine.
An Air France spokesman said Sunday that officials from France's BEA air crash investigation unit and engineers from Airbus and the US-based engine maker were flying to Goose Bay in eastern Canada where the plane landed.
"The cabin started vibrating. Someone screamed, and from there we knew something was wrong," passenger Sarah Eamigh told Canadian broadcaster CBC News about the incident in the skies above Greenland on Saturday.
"We saw the cabin crew walking through the aisles quickly, and we heard an announcement from the captain that said one of our engines had an explosion," she added.
All passengers were expected on Sunday morning to complete their journeys to Los Angeles aboard two planes sent by Air France to the Goose Bay military airport, which is used as a emergency landing spot for transatlantic flights.
"All of the 520 people on board were evacuated with no injuries," the spokesman told AFP.
The cause of the problem was not immediately clear, but David Rehmar, a former aircraft mechanic who was on the flight, told the BBC that he thought a fan failure may have been to blame.
"You heard a loud 'boom', and it was the vibration alone that made me think the engine had failed," he said.
Rehmar said that for a few moments, he thought "we were going to go down".
In 2010, a Qantas A380 was forced to make an emergency landing in Singapore when one of its Rolls-Royce engines failed, causing the airline to ground its fleet of the superjumbos for weeks.
Another passenger on the Air France flight, John Birkhead, told the New York Times that he and his wife had just stood up to stretch when they heard
"We were just stretching and talking, and suddenly there was an enormous bang, and the whole plane shook," Birkhead, 59, said. "We were lucky we
weren't tossed to the ground."
Passenger Miguel Amador posted video footage apparently filmed from a window of the plane showing the damaged engine.
"Engine failure halfway over the Atlantic ocean," he wrote.
Passenger Pamela Adams said everything on the flight had been normal "and suddenly it felt like we had run into a jeep in the middle of 35,000 feet high", she told CBC News.
She said she was "jostled" and the plane dipped slightly "but the pilots recovered beautifully".
"There wasn't the panic that I would've expected," she said, praising the pilots for the way they handled the incident.
Air France operates 10 Airbus A380s, the largest passenger planes in the world.
Their version of the plane uses GP7200 engines, a giant turbofan built by General Electric and Pratt and Whitney of the US.
Sales of the mammoth A380 have been sluggish and Airbus has said it will reduce production in 2019 to just eight of the planes.
In 2015 the company produced 27 of them.
Nonetheless, Airbus CEO Tom Enders recently voiced confidence in the future of the plane.
By AFP's Isabel MALSANG