Vietnamese officials objected to the plan during a visit by Hervé Morin, the first visit to the country by a French defence minister since 1954, when France was defeated at Dien Bien Phu.
"We do not wish to create a precedent," the official told French press agency AFP, requesting anonymity. "One never knows if one day another former foreign soldier would want to do the same thing elsewhere in the country. That would be sensitive and complicated.”
Bigeard headed a parachute battalion and was dropped into the French base of Dien Bien Phu ahead of the historic 56-day battle in 1954.
France was defeated, paving the way for Vietnam's independence. Morin said his visit was "highly symbolic". He said he did not raise the matter of Bigeard's ashes but offered to help Vietnam upgrade its forces.
Hanoi has already bought radar, helicopters and transport aircraft from France, according to Morin.
"There is a very strong demand from the Vietnamese authorities for us to be able to participate in the modernisation of the Vietnamese army," he said. "We indicated that France was politically ready to respond to the demands of Vietnam."