The new wave of Audax clubs are similar in conception to the French cylotouriste clubs. Those French clubs have an over-arching federation, which is now called FF Velo, whose name is on the shirt, as a sponsor. The new town that St Quentin is a part of used to feature heavily, as it put money into PBP, and provided support services.
The intermediate controls are generally run by a federated club, much as the CTC district might take a leading role in an LEL control. So everything ACME does in getting its club members around PBP is replicated around France. As Ivo pointed out upthread, some areas of France took the pre-qualification seriously. But in 2011 the quotas that were envisaged never came to fruition, and in 2015 the pre-qualification didn't bite.
Those countries who had experience of LEL 2013 and 2017 got their ducks in a row, and did 600s and 1,000s. There were French riders at LEL 2017, but not many, as they hadn't got to grips with the entry procedure.
I've done an event called 'Semaine Federale' a number of times. That's a week of Audax-Like rides run by FF Velo in different parts of France every year. It's about twice the size of PBP, and features many familiar faces. It kicks off with a bit of very French ceremonial featuring local dignitaries and the President of FF Velo. The health of the event can be judged by who is on the podium. If the region, the department, the city and the local communes are represented, all is well.
PBP in the past has had ambassadors, and at one point Jacques Chirac, when he was Mayor of Paris, on the podium. This time there was the Mayor of Rambouillet, and the President of FF Velo. So at the same time PBP is becoming international, it is becoming more dependent on a federation of local French cyclotouriste clubs.