The train takes only one hour. I believe we went from Gare de Nord.

Paris-Fontainebleau goes from Gare de Lyon!
Takes about 45 min. only depending on the train.
Several trains per hour.

Thanks for the information. My son and I will be going to Paris in a few months. I have been before and am fairly familiar with Paris, but did not know how to reach Fontainebleu by train. My son is quite interested in Napoleon and very much would like to visit Fontainebleu.

You might want to consider taking a guided bus tour to Fontainebleau.
I don't usually take those "canned" tours, but the one we took was handled by a very well informed guide. The trade off for me was this: I had to go at the tour's pace, but I got the convenience of the bus plus the expert services of the guide. She knew her stuff and could answer just about every question I could think up. I never studied Napoleon's military campaigns in any detail, so I don't know what she knew there. But she knew the history and the stories of Fontainebleau.
If you are into the history of France, then Fontainebleau is indeed a rewarding place to visit. It is full of the history of the monarchy as well as the empire.

Please be careful when you arrive at Fontainebleau station as the castle is at the other end of the city.
You should look for a taxi (or walk 30 minutes)

For train service, go to : http://voyages.sncf.fr/
Fontainbleau is closed on Tuesdays. As mentioned, you can take a train from Paris's Gare de Lyon to the Fontainebleau-Avon station, then catch a Cars Verts bus, or a taxi, to the chateau