"Around 125,000 households were affected at the height of the incident," it said.
Government ministers have warned of possible power outages in case of a gap between supply and demand, which they said would last no longer than two hours and be flagged in advance.
State-run utility EDF, a parent company of Enedis, is racing to get nuclear reactors hit by corrosion problems back on line.
The mayor of Paris Centre, Ariel Weil, confirmed the general breakdown on Twitter. "Power cuts have just taken place in the 4th and 5th arrondissements," he said.
Later, Weil added: "I confirm a general breakdown but @enedis confident of a rapid return to normal everywhere."
According to broadcaster Franceinfo, Paris firefighters confirmed that citizens had contacted them due to the power cuts in the four regions. Noting that the incident seems to be related to a transformer failure on Enedis' side, firefighters signaled that the situation was improving.
Around 125,000 households were affected at the height of the incident, the RTE Group, the manager of the electricity transmission network, said on Twitter.
