The damage to the bust which dates from the 19th century and is located in a park in Pau, near the Pyrenees and close to the Spanish border, was discovered during a police patrol.
The word "Nazi" had been scrawled on the statue. It was cleaned immediately and a probe opened.
France's overseas territories minister Ericka Bareigts condemned the vandalism, writing on Twitter that the memory of slavery must be respected.
The move was partly in response to frustration among members of France's black community over what many consider the country's overlooked involvement in the slave trade.
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