Apparently tax farming has been a fairly common practice throughout the world. I doubt that this is because all the countries were in communication with each other.
What political, economic, or institutional facts made tax farming appear to be a good idea to these different regimes? Are there any general reasons for it? Similarly, once tax farming was established how did regimes move from that to other forms of taxation? How were tax farmers actually able to collect taxes?
No existing answers for your first two questions relating to the ottoman or french system so it would be great if somebody could answer that
However in my searching, there were answers about the roman method of tax farming if that interests you
https://www.reddit.com/r/AskHistorians/comments/3oiqi4/what_was_the_roman_tax_system_like/