The bullet went through the canvas of the tent, where drinks were being made. It passed through a waiter's thigh and lodged in another person's calf.
The injuries were not life-threatening.
Mr Hollande was inaugurating a new stretch of railway when a gunshot was heard. He interrupted his speech for a few moments but reports say there was no panic.
"I hope it's nothing serious - I think not," Mr Hollande said as he paused his address to ask whether anyone had been hurt.
The president later visited the injured - the head waiter of a local hotel and an employee of a railway maintenance company.
One local report said the safety catch of the sniper's weapon had been unlocked, allowing the gun to be discharged accidentally.
Local government chief Pierre N'Gahane said a judicial investigation had been launched.
Asked if the officer had fired accidentally, he was quoted by the Associated Press news agency as saying: "Yes, without doubt."
The marksman is based with a special protection unit in nearby Poitiers, officials said.
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