At the height of the pandemic, revenues fell by 95% and the Air France airline was losing €15m (£13.5m) per day.
Air France does not expect that activity will return to its pre-pandemic level before 2024.
The group’s flagship airline expects to have cut more than 6,000 jobs by the end of 2022, out of a current total of 41,000 staff.
“Natural departures”, such as retirements and employees who leave of their own accord, are expected to make up about half of the reductions at Air France.
Its sister airline Hop! will see 1,020 jobs cut over the next three years. It currently employs more than 2,000 people.
The company said: “Air France and Hop! are working together with the unions to implement plans that give priority to voluntary departures, early retirement arrangements and professional and geographical mobility.”
Air France also said that a wider “reconstruction plan” would be presented at the end of July, along with one for the wider Air France-KLM group.
Union members and staff staged protests at several sites across France on Friday, including outside the company’s offices near Roissy-Charles de Gaulle airport.
The French government has pledged billions of Euros to support Air France-KLM and the wider aviation industry as demand for travel has crashed as a result of coronavirus-related lockdown measures.