He also confirmed that he had taken cannabis, an admission he first made during the presidential election in 1995. "I did it once in the United States, with a young woman, and I think once in France," the Socialist Party general secretary said.
Mr Jospin, 59, was speaking to the unconventional current affairs programme, L'Autre Journal ("the other news"), on the cable television Canal Plus.
Cannabis should not be fully legalised, he said. But criminal penalties for its possession or sale should be weakened or removed.
If Mr Jospin wins the election - which seems unlikely, on present form - France would therefore become the first large country in the world to condone the taking of cannabis.
His proposal would bring France in line with the Netherlands, which has had a running battle with the present centre-right French government for its alleged laxity in preventing cannabis from being traded through Belgium into France.
"Legalising sounds like justifying, penalising is absurd," Mr Jospin said. "I think we have to find a line somewhere between the two."
This implies something like the situation in the Netherlands, where cannabis remains technically illegal but the possession or sale of small quantities is permitted.
The latest poll forecast that the centre-right government would get between 311 and 331 seats, and the Socialists and Communists between 219 and 245.