My wife and I have reservations on the EuroStar from Paris to London on the 12:13PM train. If we arrive at Gare du Nord an hour or so earlier than we planned, is it possible to catch an earlier train without buying new tickets?
Maybe.
Eurostar tickets operate more like airline tickets than normal train tickets. Some tickets are fully flexible, some can be changed at a price and the cheapest are not changeable at all. If your ticket is flexible you'll have to change it at the desk when you arrive rather than just getting on the earlier train.