You can probably book Paris-Moscow and Moscow-Beijing from Russian Railways website. You'll need some visas to be done in advance. Better make a few stops along the way.

You can buy tickets for Trans-Siberian Railway at http://eng.rzd.ru/ , English website of Rossiyskie Zheleznye Dorogi.

I highly recommend looking through this site which extensively covers travel by train. http://www.seat61.com/

I've travelled by rail through Russia, Kazakhstan, Uzbekistan and Kyrgyzstan. It's not always easy to buy (cheap) tickets online or in advance outside of Russia but it's worth taking the risk and buying in-country for the experience of the 3 + day journeys