The letter, a copy of which was obtained by Reuters, was written by the CFDT, CFE-CGC, CGT and FO trade unions.
The French government is working on a project, called "Hercules", to ringfence EDF's nuclear arm from the rest of the power giant, and it is in talks with the European Union on the matter.
However, the 'Hercules' project has raised concerns about job security among employees, who fear that a split between the EDF businesses could result in job cuts.
The French state holds a stake of around 83.7% in EDF's share capital.
(Reporting by Benjamin Mallet)