It's hard to hitchhike on trains. But there are ways to get free train rides.
If you're in an organised hitchhiking competition...
...then it is very possible. Choose your train and wait at the platform. When the train arrives, work out who the conductor is and run up to him/her. Explain your situation (using an 'international language' such as English often works best, often better than speaking the conductor's native language), show them some documentation for your competition and don't be afraid to beg. Telling a story about a dangerous experience two hours ago on the roadside (true or not...), and how much you want some safe and secure travel after the traumatic experience, works well. By this time, the train is now running nearly a minute late and there is a good chance that the conductor will say Yes, because he needs to end the conversation and keep the train moving. So get in, sit back and relax :).
Tom and his two team-mates tried using this trick when travelling through the Netherlands and Germany on Sheffield University's 'Bummit' hitchhiking competition. 9 out of 13 conductors we asked said Yes, and let us travel as much as we needed on their trains. It didn't work when the train was either crossing an international border, or it was a high-speed train, or the conductor just didn't want to bend the rules...
There are no fines on trains, the inspector checks only a few times during a trip (even on those very small trains), and if he finds you without a ticket, he simply kicks you out, although some are nice enough to let you ride for free. An exception is Eurostar trains, they will want you to pay, but if you have no money they will still have no choice but to let you go.
When leaving big cities, trains sometimes get heavily checked, so you may have some difficulties. If you are found with no ticket, no ID and no money, he may simply kick you out, but he is more likely to call the police - but the police are not a problem since you can simply give them fake data about yourself and they will let you go. TGV trains are far better than Ter trains, since there are few stops and they are much faster.