Which French-American writer is known for his works that depicted the rural life of colonial America?

The correct answer is J. Hector St. John Crevecoeur, who is renowned for his writings that illustrate the rural life and experience of colonial America. His most famous work, "Letters from an American Farmer," provides a vivid portrayal of life in the New World, focusing on the challenges and rewards of agricultural life, as well as the cultural mixing of European settlers and Native Americans. Crevecoeur's insights helped shape the perception of the American identity at that time, emphasizing themes such as individualism, the natural environment, and the concept of the "American Dream."

The other figures listed, while significant in their own right, do not focus on the same themes of rural colonial life in America. Voltaire was primarily a French Enlightenment writer known for his critiques of society and philosophy rather than a focus on America. Alexis de Tocqueville is celebrated for his work "Democracy in America," which analyzes American political culture rather than rural life specifically. Louis Frémin, though he contributed to French literature, is not well-known for works focused on the rural aspects of colonial America. This context underlines why Crevecoeur is the appropriate answer.