The air traffic controller responded: "I've seen on the radar, it swayed to the left."
Air France said it "regrets the discomfort felt by customers".
French air safety officials described it as a "serious incident" after retrieving data about the aborted landing.
Officials from the Bureau d'Enquêtes et d'Analyses pour la Sécurité de l'Aviation civile said officials had notepad: "Instability of flight controls on final, go-around, hard controls, flight path oscillations."
AirLive.net first reported the aborted landing. A spokesman told the website: "Air France confirms that the crew of flight AF011 on 4 April 2022 from New York JFK to Paris-CDG aborted their landing sequence and performed a go-around due to a technical incident during the approach.
"The crew mastered the situation and landed the aircraft normally after a second approach. Air France understands and regrets the discomfort felt by customers."
Shares in Boeing fell more than 5pc in New York on Wednesday.
The widebody Boeing 777 is a mainstay of British Airways' long-haul fleet. The UK flag carrier operates more than 50 such jets.
Nearly 13 years ago Air France flight 447 from Rio de Janeiro bound for Paris stalled and crashed into the Atlantic Ocean, killing all 288 passengers and crew.
The remnants of the Airbus A330 were finally found on the ocean bed by investigators three years later.
In 2000 an Air France Concorde crashed shortly during take-off from Charles de Gaulle airport with 109 fatalities. It was later found that the supersonic passenger jet had hit debris on the runway, bursting a tyre which then threw parts of its landing gear into fuel tanks located under its left wing.