What is the most appropriate word or phrase to call all the books, theater plays, movies, etc. that a culture has produced and is still producing? For example, "the products of the French culture."
Cultural heritage ("national heritage" or just "heritage") is the legacy of physical artifacts (cultural property) and intangible attributes of a group or society that are inherited from past generations, maintained in the present and bestowed for the benefit of future generations. Cultural heritage includes tangible culture (such as buildings, monuments, landscapes, books, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage (including culturally significant landscapes, and biodiversity).
According to C. Marshall Hattersley, the word you are looking for is "Civilization."
In fact cultural inheritance is defined "the vast heritage of discovery and invention, of culture and learning, of organization whether social, political or industrial, of education and religion, of aspirations and ideals which have been handed down and developed by generation after generation ... Collectively these form the Common Cultural Inheritance of humanity, or more shortly, Civilization.” (This Age of Plenty, by C. Marshall Hattersley, p. 232.)
Civilization, under the above perspective, is considered to be the latest stage in the evolution of cultural heredity.
(the arts) the various branches of creative activity, such as painting, music, literature, and dance: the visual arts
The full phrase could combine the group defining adjective with arts as in the French arts.
If this seems too limiting because it may seem to focus on just fine arts, it could be expanded to the French fine and technical arts
Wikipedia: Cultural artifact (or social artifact) is a term used in the social sciences, particularly anthropology, ethnology, and sociology for anything created by humans which gives information about the culture of its creator and users.