Hmmm...those trains I step onto are (a) typically high speed and (b) quite often "international", though the concept really doesn't make much sense in the Schengen Area.

Are you talking about the Eurostar service from London (I remember the Waterloo station, though I hear it has moved to St. Pancras). That's the only one I can think of that fits your description.

The Thalys from Cologne to Paris via Belgium is/was also simple walk on walk off with normal train stations.