I wrote this to you in reply to your PM, but maybe its good to keep the discussion on the forums, in case other people wonder the same later.
The EU does not have so much to do with intra-national travel laws, however there is another union, under the Schengen agreement, That more or less says that there will be no border controls for trade or tourists. This is nice for people living in the area, but for those of us from outside, its actually really lame. As a US citizen, you are allowed 90 of every 180 days in the Schengen Area, which consists of 26 countries (most of western Europe). EU does not equal Schengen however, and vice-versa. There are some countries that are Schengen and not EU (Switzerland for example, as well as some of the micro states like Andorra). There are as well countries which are EU and not Schengen. The UK for example. Sucks for you.
The UK, in exchange for having the best travel allowance in the world for it's citizens, has some of the strongest immigration controls. In Calais is this giant no borders camp as well, so you can be near sure that you WILL be controlled trying to take the train into the country (you are not the first immigrant to try).
As well, if you are not even paying for your way in, it is quite likely that you have no exit plan, and they will indeed hassle you more than just fining you for not having a ticket. I have not taken this train, but when I flew into the UK in 2009, I was held in immigration holding for 14 hours, before being deported. Its not quite the same as a normal deportation when you are refused entry (for not having a flight out of the country booked upon arrival), but it is indeed a bit of a pain in the ass. Maybe it's easier on the train, but likely you will be put on the next train back to France, and quite possibly controlled again for entering Schengen (as well, you will likely have an "escort" officer with you).
Good Luck, let us know how it goes. I guess you have a bad day ahead of you if this is your plan.