im assuming that eurostar is the same as airports, so the 100ml liquid ban would be in force, so no bottles containing liquids over 100ml (drinks, shampoo, aftershave, etc...) in hand luggage.
whenever i go abroad i keep a change of clothes in my hand luggage, just in case my suitcase gets lost, and ill take a book, or mp3 player to keep me occupied on the journey.
there are dimensions for hand luggage, which is dependant on who you are travelling with, but most of them are lenient, as long as its not massive so a backpack will almost certainly be fine