Fontainebleau

First, I'd get a new France book.

https://en.wikipedia.org/wiki/Palace_of_Fontainebleau

Take the train to avon/fontainebleau and get a bus to the chateau from there. Make sure to go on a day it is open. Get two tickets unless you have a transportation pass, so you have one in hand for the return since it is not a well staffed station. Very easy day trip.

Fountainebleau chateau is worth seeing, particularly if you are interested in Napoleon. While not quite as spectacular as Versailles, it is still very impressive. To get there take the train from Gare de Lyon. Go to ticket window and ask for round trip ticket for Fountainebleau. (it's a day pass that is good for the train, bus, metro) Find the correct train, validate your ticket at the machine first. Trip is a about 40 minutes to the town. Get off train and follow the crowd to a parking lot nearby that has a lot of buses. I believe the #1 bus is the one you want, should say Chateau on front. Ask driver to be sure. It's about a 2 mile bus ride through center of the town to the chateau. Going back to Paris, get on bus outside of the chateau and return to the train station. It is very small, and virtually all trains stopping there will go to Paris. Verify this.
Looking at latest Rick Steves Paris guidebook, I don't see instructions for going to Fontainebleau. Perhaps other guide books have this.
Enjoy!

Thank you for the train info. I have the current Rick Steves France 2017, as well as his 2010 book, and couldn't find anything on Fontainebleau in either of them. I did go back to a 2011 RS book I have for Paris and found a little info in there.

On this site under Watch, Read + Listen, click on Watch the Live TV show and then on France. There is a segment there on Paris Side trips. They go to both Fontainebleau and Vaud-le-Vicomte (my fav) there.

Absolutely, Fontainebleau is worth seeing. To get there follow the accurate suggestions above. Walking back to tjhe station from the chateau and centre ville takes about 40 mins. There is also a Napoleon Museum on Rue Honore, about a 30 mins walk from the chateau, well worth seeing at least once, all the more so if you are into Napoleonic history. The topic of the post cards focus on Napoleon and Fontainebleau, where he lived inside the chateau, where he signed his first abdication, etc, the courtyard where he said farewell to the Guard, les grognards in the presence of the four Allied officers serving as Commissioners.

If you have or getting a navigo pass , it's good for the train and the bus ride to Fontainebleau. About a 40 minute train ride and 10-15 minute bus ride . Well worth it ,

Make sure you take the time to stroll around the grounds, they are beautiful. The little cafe's just down the block from the Chateau are great.

If you have the Navigo Decouverte Card, the train is covered as well as the bus to and from the station & Chateau. Also, if you have the Museum Pass it covers the Chateau as well.
Enjoy your trip.

If you don't have a Navigo, carnet tickets for central Paris travel are also valid on the local buses in Fontainebleau.