The correct answer to this open question is the following.
The term that refers to any society based on farming is "Agrarian Society."
When we are talking about an agrarian society, what we mean is that society bases its economy in farming, producing cash crops to trade or to export in order to make a living. Many times the society or the country's main products are agriculture products, not industrial products. When that is the case, we are referring to it as an agrarian society.