Audax before 1904 wasn't formalised. Only Audax Italiano existed then and I'm not sure exactly what happened with them or how they ran or recorded things.
Once Audax Club Parisien was formed in 1904, then the whole circus started, with brevet cards, routesheets and everything else. Have a look at Jacques Seray's PBP books or Bernard Deon's UAF book (in French) for pictures of early brevet cards and routesheets. There hasn't been very much in the way of change since Audax began. Changes in maximum time for a 200km brevet of 14 hrs or 13.5 hrs is just fiddling round the edges; the basic concept hasn't noticeably changed.
The reason the ACP and other country's BRMs have mandatory routes now was because they grew out of Audax pre-1921 which also had mandatory routes. Pre-1931, Audax brevets were ridden at 18 kph between scheduled rest stops. The first PBP brevets were in 1931 and PBP31 Audax was ridden at 20 kph. The UAF 22.5 kph riding average came in after World War 2. Other than adding new awards every few decades and a couple of new brevet types (Fleche Velocio and Super Randonnee 600), the ACP have changed remarkably little over the years.