Comment by lainga

To add to the other comment, the Eurotunnel Shuttle does this but for the Channel Tunnel.

https://en.wikipedia.org/wiki/Eurotunnel_Shuttle

Flatbeds would be a bit risky, you can see in both this case and Amtrak's case they are enclosed cars. Apparently the Shuttle is one of the most comfortable rides in the world - as there are three layers of suspension (train carriage, carriage-vehicle mounting, and vehicle suspension) between you and the rails beneath.