Their armoured vehicle, in a convoy of four vehicles, was blown up by an improvised explosive device in the Tagab region, the Elysee Palace said in a statement.
The wounded soldiers were immediately evacuated to Kabul military hospital by helicopter, the defence ministry said.
The death of the corporal from the 19th engineering regiment brings to 73 the number of French troops who have died in Afghanistan since the end of 2001, 21 of them this year alone.
France has some 4,000 troops in Afghanistan.
Afghanistan is in the grip of a deadly insurgency launched in late 2001 by the remnants of the Taliban whose regime was toppled in a US-led invasion after the September 11 attacks.
There are around 140,000 combat troops currently in Afghanistan to fight the insurgency, of which 100,000 are from the United States.