A man aged in his thirties stepped onto the grave and kicked the base of a 1.5-metre (4.9-feet) -high stone cross at its head.
A man aged in his thirties stepped onto the grave and kicked the base of a 1.5-metre (4.9-feet) -high stone cross at its head, causing the cross to topple over and break, they said.
The gravestone itself was undamaged, they said.
The simple grave, located in the village of Colombey-les-Deux-Eglises in the northern French department of Haute-Marne, draws tens of thousands of visitors each year.
The site is under round-the-clock video surveillance, Frederic Nahon, the public prosecutor in the town of Chaumont, said.
De Gaulle led the Free French Forces in London from 1940-44 and reshaped the country's political landscape after the war, founding the Fifth Republic in 1958. He remains a revered figure to many French people.
De Gaulle died in 1970 shortly before his 80th birthday. He is buried next to his wife Yvonne and daughter Anne.