Four of the eight undersea cables beneath the Channel were damaged during a storm on November 20 and industry sources say it could lead to higher energy prices in France in the coming months.
"We think it's a ship or even ships, but we can't say that for certain until the investigations have concluded," a National Grid spokeswoman told AFP.
The interconnector's maximum capacity will continue to be down from two gigawatts to 1GW until the completion of work to fix the fault, which is expected to last until the end of February.
2GW is enough to power a million homes.
Flows were running below 1GW so the fault went undetected until Saturday when they increased.
The capacity reduction means Britain will not be able to export as much surplus energy.
"During the peak, we can still get energy in and can still get other options to call upon, but it will dent our ability to send power to France," the National Grid spokeswoman said.
The cables tend to be exporting power to France, except during the evening peak in Britain when people get home and turn the lights on.
The cables, which are buried up to three metres below the seabed, will have to be taken up by barges and repaired in a technical and time-consuming operation that takes roughly three months to complete.
The British mainland has four undersea interconnectors going to France, the Republic of Ireland, Northern Ireland and the Netherlands.