A robot submarine will locate the ends of the cables on the sea bed and bring them to the surface to be re-connected.
They were cut within 5 minutes of each other, possibly by a trawler net.
Egypt says it has been able to restore most of its communications by re-routing services, but other parts of the Middle East remain badly affected.
Experts have warned that it may be days before the fault is fixed and that the knock-on effect could have serious repercussions on regional economies.
Experts from France Telecom Marine arrived at the site of the damage to the SEA-ME-WE4 and SEA-ME-WE3 lines onboard the cable ship, Raymond Croze, at 1330 GMT on Sunday, spokesman Louis-Michel Aymard said.
They then sent a remotely-operated submarine robot called “Hector” to the sea bed to begin the search for the two ends of each line.
It is unclear how long repairs will take, as a ship could have dragged the cables several kilometres from their normal positions.
Once located, the cable ends will be brought to the surface by the robot and repairs will be carried out in a special facility on the ship – a process that could take days.
“We have to fix the cable fibre by fibre, and it’s a very huge cable,” Mr Aymard told the Associated Press.
France Telecom said it expected to repair SEA-ME-WE4 by 25 December and SEA-ME-WE3 by the end of the year.
A third line, operated by FLAG Telecom, was also cut and will be repaired by another ship.
In January the same line was damaged off Egypt’s Mediterranean coast, severely disrupting internet and phone communications for many in the Middle East for days, although only two lines were snapped then.
A few hours before the three lines were cut, a suspected sub-sea earthquake damaged a local GO cable to Malta, severely disrupting communications to the island.