The "Ramses 2016" military and naval exercise is being held off the coast of the Mediterranean city of Alexandria and are expected to last for several days, the army said on its Facebook page.
Paris announced the manoeuvres Tuesday saying the French aircraft carrier Charles de Gaulle, which is being used to launch air strikes on the Islamic State group in Syria and Iraq, would also take part.
The drill is aimed at "sharing our expertise with the Egyptian military... one of our main Middle East partners," the French defence ministry said at the time.
The Egyptian army said a French multi-mission frigate purchased by Cairo last year would also take part in the drill along with Rafale combat jets and F-16 warplanes.
In 2015, Cairo signed a multi-billion euro deal to purchase from France 24 Rafale fighters, of which six have been already delivered.
On December 19, the Charles de Gaulle carrier took command in the Gulf of the naval contingent operating as part of the international coalition fighting the jihadist IS group.
The French-Egyptian manoeuvres are taking place amid Western concerns over the growing influence of IS in Libya, a country bordering Egypt.