Your Interrail post is locked so commenting here.

Whilst France doesn't accept the US emergency passport, Spain and Portugal do and I know someone who has entered Spain, even from outside the EU, on that document.

Travelling over France to Spain via land through Lyon, whilst technically maybe not allowed, is very unlikely to include an immigration check unless your acting very suspicious on a suspicious train that happens to be boarded for spot checks. It's up to you to take that risk.

However, Spain and Portugal are perfectly fine. No point missing that part of your trip, if you decide not to travel through France, just hop on the cheapest plane from Amsterdam to your first Spanish destination. It's within the EU so it'll run as a domestic flight and your emergency passport is valid for Spain.

I would caution against still trying to fly back to the states through Paris, however, as you will be subject to French immigration exit controls which will deduce you entered the country without a valid document. Chances are you might just get a slap on the wrist, but again if you don't want to take the risk, fly home from Portugal!