It was a 0.3 percent increase over May, when the rise was 0.7 percent from the previous month.
"These figures confirm a fragile recovery," the ministry said in a statement. "The steps that the government has taken have helped to stem the increase."
Struggling with a stagnant economy, President Francois Hollande's deeply unpopular Socialist government has so far been unable to cut unemployment.
About 474,000 new jobseekers have been added on to the books since Hollande took office in May 2012.