The 43-year-old died from his wounds at the scene despite efforts by the emergency services to save his life, Ouest France reported.
The employment agency, named Pôle Emploi in French, at Nantes Est remained closed on Wednesday and police were on the scene.
It is not yet clear what drove the man to set himself on fire but it has been reported that he was angry that he believed he was entitled to unemployment benefits and he was angry that his application had been rejected by the agency.
The man sent a letter to several local journalists on Monday warning them of his intention to set himself on fire this week, French media reported.
A 51-year-old jobless man had also burnt himself to death near Paris in August. In October 2011, an unemployed man held hostage the directors of a job centre in Paris. He wrote to the media saying he could no longer cope with being unemployed.
"The system needs to change"
Philippe Baot from CGT Chômeurs, a branch of the CGT trade union which fights for the rights of the unemployed told The Local the "inhumane" benefits system and its rules had caused the man's break down.
"This man should have been given money by the Pôle Emploi because he had been working but the staff stuck to the rules and those rules caused this incident. They need to change.
"The system is too complicated and its inhumane. The Pôle Emploi has cut relations with those seeking jobs. Everything is done on the phone or internet which excludes a lot of people," Baot added.
The number of unemployed has risen steadily in France over the past 20 months, and could soon reach the high record high set in January 1997 of 3.2 million. Last year the rate broke the symbolic 10 percent barrier and at the end of last year it was at its highest rate in 15 years.
Baot believes many unemployed people are being left behind as the crisis deepens.
"Distressed unemployed people come to see us all the time. We are not talking about homeless people, these people are just out of work. They feel totally excluded, its a form of social suicide.
"The government needs to reform the benefits so it's managed better and its less complicated," he added.
Labour Minister Michel Sapin expressed his condolences over the "horrifying" act while the state employment agency said it had "looked into possible solutions" to help the man.
French President François Hollande has vowed to stop the jobless rate from rising by the end of 2013 and has declared this year "the great battle for jobs".