Where is your second flight to? (I presume your 6 am arrival is from the States?)
First of all you have to calculate IF your flight arrives on time, 1hour if all goes well to clear immigration and pick up your bags and walk through customs. Sometimes 1.5 hours. anyway, if you arrive on time, it's 7 a.m.
For a 2 pm departure, you need to be at the airport at noon.
So your real window is 7 am to noon, from my perspective. You have NO time to be taking trains and making changes, and the Chateau in Chantilly is a bit of a hike from the train station (not too far for anyone who wants to do it or who's taking the better part of a day to go there , but too far for you to be dealing with.)
So you need a taxi to Chantilly - say it takes you 45 minutes to get there. It's now 8 am or 8:30. Guess what - the chateau doesn't open until 10 am (or 10:30 in low season, but I presume you're coming in the summer). So you go have breakfast somewhere, wander around.
Then you go into the Chateau and around the grounds from 10:00 to 11:15 or so, when you need to get your taxi to go back to CDG to make it there by noon for your check-in for your onward flight.
So basically you have to decide if it is worth it to you to go through all that for little more than an hour on the grounds and in the chateau. Only you can decide!!