The name Josette is a French baby name. In French the meaning of the name Josette is: American Meaning: The name Josette is an American baby name.In American the meaning of the name Josette is: Hebrew Meaning: The name Josette is a Hebrew baby name. In Hebrew the meaning of the name Josette is: May Jehovah add/give increase.he name Josette is a French baby name. In French the meaning of the name Josette is: American Meaning: The name Josette is an American baby name.