Back in 1988, I was traveling by train from Lille, France to Amsterdam. At one point I stopped a train official to ask when we would be reaching the Belgian border, as I wanted to have my passport ready. That's when he informed me I had passed the border about an hour before.
I've never been asked for my passport in all my travels through western Europe (France, Germany, Italy, Switz. & the Low Countries), crossing borders on foot, by car, or train. Hell, twice I didn't even have to open my passport at the airport. But then I'm Canadian, and Europeans like us more. (joke, joke.).