Negotiations over how to separate EDF's nuclear arm from the rest of its activities and to fix the price at which it distributes energy to third parties have dragged on for months, with both sides initially looking at end-March as a deadline.
France is keen to pass any reform of EDF as soon as possible before the parliamentary calendar gets too busy in the latter part of the year, and campaigning for the next presidential election begins in 2022, sources have previously said.
Le Figaro newspaper reported on Tuesday that the European Commission and the French government had agreed on the need to move quickly. EDF shares had risen 4.55% to 12.06 euros by 0805GMT, with traders citing the report.
The newspaper added, without citing sources, that the Arenh fixed price at which EDF sells on nuclear power would be set at 49 euros a megawatt hour (MWh), up from 42 euros currently.
Unions including the CGT, which have met with the government in recent days, have also cited 49 euros as the likely new price.
France's economy ministry declined to comment. Talks between the French government and unions, which are fiercely opposed to the restructuring, arguing it will result in a break-up of EDF, are to continue next week.
The reform needs the green light from Brussels over possible state aid issues and whether the funding mechanism for EDF's nuclear arm is sufficiently ring-fenced from the rest of the business.
(Reporting by Patrick Vignal, Writing by Sarah White; editing by Emelia Sithole-Matarise)