Having ridden the 2003 PBP I can offer some advice.
First, just do it, it is the most amazing experience, 4500 cycling nuts from all over the world, and yes you do have to be a certified cycle nut to contemplate such a ride.
You will never every forget the support of the French people enroute, from young kids to the elderly encouraging you on, offering food and water at literally all hours of the day and night.
Training yes by all means start now, be happy with riding 300 or maybe 400km by the end of this summer. Doing this will start sorting out not only your fitness but all the other essentials such mental fitness, lights and above all being totally comfortable on your bike. All the other things count for nothing if you are not totally comfortable on your bike for hours and hours at a time.
I started preparing for the 2003 event at about this period out but really didnt do any big distances until well into 2002 but had ridden many 200km audaxes.
Comtemplate getting a suitable bike, more tourer than road bike for the long distance comfort. It MAY be a bit slower but in the long run you are better off.
From now on read everything you can about the event from the history, Charles Tarront the winner in 1891 of what was then a race in 73 hours to accounts of the ride from 2003.
From now on in the words of Fausto Coppi - Ride Your Bike - Ride Your Bike - Ride Your Bike.
Get into the mental attitude that enables you to contemplate getting out on your bike for at least 100km at any time of the day or night and in any weather conditions. You may not actually get out but the fact you can deal with that concept without throwing up your hands in horror means you are some way to the mental preparedness.
CC