The Post Office has formally denied this number.
"All the suicides are linked to the way people feel in the company,” CGT union member Jean-Luc Botella told AFP. He added that one had left a note for his wife which backed up this theory.
The worker who died at the weekend was being subjected to an audit after making an 160-euro accounting error.
His wife told AFP her husband had been worrying about work for the last six months and that she may take the Post Office to court.
The Post Office has started an independent internal enquiry.
France Télécom was hit by a similar problem in 2008 and 2009. A total of 35 workers killed themselves.