The group forecast sales volumes for the market as a whole would drop 17 per cent in the final quarter of this year in main European markets and by at least 10 per cent in 2009.
Nine hundred workers from Rennes, where the group makes its Citroen C5 and C6 models, are also to be redeployed to other sites.
In a speech on a visit to an aerospace supply company near Paris, Sarkozy said France would not leave large parts of the economy vulnerable to the economic crisis, picking out the car sector for special mention.
Sarkozy said: "I will not leave entire sectors unarmed in the face of the crisis. I am thinking about the automobile sector."
Jean-Luc Vergne, Peugeot's human resources director, said the company had to act or would put its future in danger.
Last month, the company slashed its 2008 profitability outlook and announced big production cuts to combat the sales crisis after posting a 5.2 per cent drop in third-quarter sales.
Ulrich Horstmann, an analyst at Bayerische Landesbank, said: "They had to do something. The catastrophe is that demand is going down more than ever."
Peugeot will present the plan to shed 2,700 jobs to its works council on December 2.
It has not yet set a date to present the separate Rennes plan for 850 departures.
Car sales across the world have fallen steeply as the effects of the global financial crisis have rippled out into the wider economy.
Carmakers have slashed costs and extended the usual Christmas time period when plants are left idle by several weeks to save money.
European carmakers have so far asked for $50.5bn in soft loans from the state, with Opel currently in negotiations with the German government.
GM, Opel's parent company, and other carmakers in the United States are also seeking a government bailout.
Nissan, GM and Ford all announced in October that they would cut output at their European sites.