Andy,
To qualify for PBP you need to complete a Super Randonneur (SR) series in the same season as PBP. SR consists of 200, 300, 400 and 600 km brevet rides. AFAIK you can also substitute longer rides for shorter ones (e.g. do two 400s instead of the 300 and the 400), but you do need four rides of at least these distances and you need them before July.
The Japanese event calendar for 2019 will be published shortly as Audax Japan has just had its annual meeting. Event signups are mostly handled via SportsEntry. There are about half a dozen clubs in the Kanto area, just about all of which will offer a full SR series and more than 20 clubs countrywide.
You don't necessarily have to do the rides in Japan. Any ACP-sanctioned events worldwide (e.g. US, Canada, Europe) will do. Audax Club Parisien is the organisation that homologates all the rides.
I can't guarantee that if you complete SR you will be allowed to start at PBP, but I think it's highly likely, at least for people who have done brevets before. In 2015 the PBP website mentioned a rider limit. People who have completed at least one brevet in 2018 will be able to pre-register at an earlier date which reserves a slot, with the opening date depending on the longest distance completed (e.g. 1000/1200 km first, 600 km next, etc). This will have to be converted into a full reservation by some date in late June. Without pre-registration you can do the full registration when you have done at least 3 of the 4 qualification events, with a cut-off in early July. The exact dates are not yet on the PBP website.
Personally, I am not really aiming for PBP. Completing a 600 within the 40 hours time limit is a tough one for me, as I've been too slow to be left with enough time to sleep as needed for any distance too long to ride by staying awake throughout. That is simply not going to work for a 4 day ride. So I would need a less challenging 600 km course than the one I have been attempting 3 or 4 times so far. Also my business travel schedule would have to not conflict with my brevet schedule so I could fit in enough rides and alternate rides in case of bad weather to make SR. Having said that, riding with thousands of long distance cyclists from all over the world in France, with spectacular local support, would be the experience of a lifetime.
Official PBP flyer in English here (PDF)
Thanks for all the details Joe. Really appreciate it!
Andy