Flights to/from Paris:
To get to the venue the most convenient location to fly into for most people will be Paris. In Paris there are two major airports - Charles de Gaulle (CDG) and Orly (ORY), and either works equally well. You can also fly to London (Heathrow or Gatwick), and take the Chunnel (or fly with RyanAir) to Paris. Yet another alternative is to fly to Brusselles and take the Thalys bullet train to Paris.
To get the best price the key here is to shop around! Airfares are REALLY high in the fall to winter before the following summer. They usually bottom out around February for the coming summer so keep your eyes peeled for the best fares. And if you are hoping to use frequent flyer miles, BE PATIENT. Most of the seats are already taken, but most airlines continue to open up a few seats all the way up to early January so keep trying.
Train service to the chateau to/from Paris:
There actually is train service to Saint Patrice (where the chateau is located) and it is cheap and relatively fast, but somewhat complicated. You can go directly from Paris Charles de Gaulle Airport (there is a train station right in the airport), or you can take the RER (regional) train to central Paris, spend a couple of days, and then take a train to St Patrice at the Gare (Station) Montparnasse. In either case, it will take you about 2-3 hours, including two changes of train, and cost about $75 (economy fare). You can make train reservations online at raileurope.com.
Renting a Car:
This is not for novices so if you've never driven in Europe (and you are directionally challenged), find a friend to do the driving. :) It is especially complicated to drive in and around Paris, and CDG Airport is on the opposite side of Paris from St Patrice and the Loire Valley. Once out of the Paris area, driving gets easier, but be sure and do two things - buy a France roadmap AND get GPS on your rental car. If you do drive, you will find that the rewards are worth the trouble, as this part of France is absolutely gorgeous and there are many attractions that cannot be visited without a car!