When was the first attempt to create a secular society? (a society that was intentionally separate from religion). Was the French Revolution the first to discard religion as an legitimizing force and to create secular calendars?
This question makes no sense until a "religion" is unambiguously defined. And this is difficult. Some definitions are so broad that according to these definitions, there is no irreligious society at all.
For example a remarkable book by Vercor, Humans or animals? (one of the places where I have seen a general definition of religion) includes "burial of the dead" and "ritual cannibalism" as some criteria of existence of religion in a society. I think since the beginning of history, (that is since the writing was invented) there was no society where the dead were not buried, or otherwise disposed with some ritual.
According to such broad definitions, Communism or Confucianism, or any philosophy, or a code of behavior, or system of beliefs is called religion. If you invent some narrower definition, which would exclude Confucianism, for example, then China (or parts of it, in different periods of history) is a very ancient irreligious society.
Arguably all societies are formed around institutions. Fukuyama claims, and it seems reasonable, that religious institutions were the most effective institutions between the "tribal" organization and modern secular societies.
@Alex is right that it is difficult to judge how much a given institution relies on mystical or preternatural support. American is by treaty "not a Christian nation", but our money and our governmental rituals pay repeated service to a divine being. (please don't argue the point, merely note that the evidence isn't 100% consistent). On similar grounds, I'd argue that the "secular" status of the Communist party is arguable (the repeated assertions of the role of Communism in destiny, the "incorruptibility" of Lenin's body, the necessity of quoting the Mao and other prophets, etc. Although the official party line may be atheistic, the ritual practice of the members resembles religious behavior.) Outside the Western tradition, I concur with @Alex that Confucianism is a secular institution; I admit that I am not an expert on the field and that in my experience there is no consensus on the topic.
I stipulate that "Religion" and "secular" are difficult to objectively define.
Having said that I think that the French Revolution was the first group to make a positive attempt to exclude religious institutions from the legitimacy of their government. Of course they promptly replaced it with a secular religion; it is equally valid to answer that there has not yet been a secular society.