"The reasons in favor of the 'yes' by far outweigh the temptation to say 'no,'" Jospin wrote in an article published Thursday in Le Nouvel Observateur magazine, saying he would urge his party to support it.
While flawed, the former Socialist prime minister wrote, the constitution does provide social guarantees the French left is calling for -- and besides, he added, opposing the document would put French socialists at odd with their European counterparts.
France's ruling conservatives largely back the constitution, and French President Jacques Chirac says French will be able to vote on it during a referendum next year.
But the Socialists -- who trounced Chirac's UMP party in regional and European elections this year -- are divided on the constitution.
Socialist party head, Francois Hollande supports it. But another former leftist prime minister, Laurent Fabius, recently weighed in against it.
"A well-reasoned yes," France's conservative Le Figaro newspaper wrote of Jospin's position.
But Socialist party lawmaker Manuel Valls described Jospin's backing as a "yes of resignation," in comments to the daily Le Parisien.