On the trains you’ll find compartments available to store and secure your luggage, either upon entering the train cars or in overhead compartments.
It’s in your best interest to label (as clearly as you can) all of your luggage with your name and phone number on it to avoid any mix-ups. You won’t have a problem finding a place to secure your belongings.
Luggage on Eurostar
As an example we can talk about your luggage on Eurostar that allows big luggages (larger than 85cm/33” at its maximum length) but they’ll be transported by Eurostar’s registered baggage service. At Eurostar trains you are allowed to carry 2 medium sized luggages (less than 85cm/33”) and if you have more than that, you’ll have to pay 25 Euros per extra luggage on the train.