The Afghan soldier accused of the killings said he did it because of a recent video showing US marines urinating on the bodies of dead Taliban insurgents.
On Saturday, Longuét said he had been told the Afghan soldier who killed the troops was a Taliban infiltrator, but Karzai did not mention this allegation.
Karzai expressed his sadness over the incident and said it was a matter of concern that for the second time an Afghan army soldier had “turned his weapon on French soldiers”.
Six French soldiers have been shot dead in just three weeks by Afghans they were training.
The statement said Longuét had thanked Karzai for his condolences and assured his country’s continued assistance to Afghanistan.
Earlier on Sunday, Longuét and General John Allen, the US commander of foreign troops in Afghanistan, presided over a solemn repatriation ceremony for the bodies of the four French troops at a snowy Kabul airport.
The four coffins, accompanied by photographs of the fallen soldiers, were draped in the French flag before being carried into the French presidential jet.
Twelve of the soldiers wounded in Friday’s attack have already been evacuated to France. Two others, too badly wounded to travel, are being treated in the American military hospital at Bagram base in Afghanistan.