The figure represents just under 10% of the total workforce of 53,000.
The job cuts form part of a restructuring plan to restore profitability, in the face of increased competition and soaring fuel costs.
Air France says it is hoping to avoid compulsory redundancies through natural turnover and voluntary redundancies.
The company estimates some 1,700 jobs could be lost through natural turnover.
Air France, one component of the French-Dutch air carrier Air France-KLM and the first air carrier in Europe, launched a major cost-saving programme, Transform 2015, earlier this year, after posting a loss of 809m euros (£653m) for 2011 and a first quarter net loss in 2012 of 368m euros.
Shares in Air France-KLM shot up by 6% after the job cuts announcement, the AFP news agency reports.