Accidentally skipped customs…now what?

Did you bring anything that you need to declare?

Although you should have passed through customs after baggage claim, I don't know how you managed to avoid it.

You went through immigration in Paris, right? There are no checks between Paris and Amsterdam; you probably passed through an area with customs offices after baggage claim in Amsterdam but those are rarely manned.
So, you have nothing to do.
Unless you did not go through immigration in Paris, in which case...no idea.

Customs in Europe is not like the US. You simply walk through a green door if you have nothing to declare. No one stops you. You probably walked through the green door and didn't even realize it. You will not get in trouble.

Reminds me of this video where the YouTuber was locked between points of transfer in Heathrow: https://www.youtube.com/watch?v=7Ldv0qjaaNE

So long as you immigrated in to Europe in Paris (ie- had your passport checked), then you had nothing else to do in Amsterdam- Paris to Amsterdam was essentially the same as a domestic flight from state to state in the US.

Right. You would have entered the Schengen in Paris - you had your passports checked there, right? - so it was OK to just walk out of the Amsterdam airport without further checks.

https://home-affairs.ec.europa.eu/policies/schengen-borders-and-visa_en

Thanks to all of you who responded so quickly! Yes, we did have our passports stamped in Paris. I am relieved to know we did not break any laws and can now relax and enjoy our vacation.

You didn’t skip anything you should’ve done because you can’t get out. There’s no secret door you found that would’ve let you out. Don’t worry about it. Go on with your vacation (by the way customs is always a walk-through unless you’re a smuggler. And that’s what you did. At some point you walked right past some person who was standing there looking to see if you looked like a smuggler and if you were, he would’ve pulled you over. When you come back to the United States, it will be exactly exactly the same process. You will get your luggage and you will walk past someone standing there.)

It's exactly like that if using a connecting flight once within the Schengen borders. I do it all the time arriving back in France and have never figured it out--

except one time one large suitcase filled with household supplies and Costco vitamins was four days late getting to us. I think French customs took a peek during transit.

Folks above are correct. You are fine. No need to worry and you didn't break any rules.

In Europe we have the Schengen Area, which is a free travel area, and within it you do not need to pass immigration. But the Schengen Area is not contiguous with the European Union.

And this leads to some complications. If you travel from Paris to Amsterdam you have neither Immigration, nor customs to pass through. But if you travel from Paris to Zurich you need to go through customs, but not immigration, as Switzerland is within Schengen, but not within the EU. Fly from Paris to Bucharest, and you need to pass immigration, but not customs, as Romania is in the EU, but not yet in the Schengen free travel area.

And for this reason in Europe immigration and customs have been split, so it is not like in the US. You do immigration when you arrive in the Schengen Area, (which in the OPs case was Paris) and you do customs after you pick up your luggage (in this case in Amsterdam). But customs is just walking through the right channel. Some airports have a separate "blue" channel for passengers coming from other EU countries, but in most cases passengers originating from EU countries just use the Green channel, which is also the channel you use when you come from outside the EU and have nothing to declare. If you have something to declare you take the red channel.

The tags attached to your luggage have a green edge when they have been printed at an EU airport, so the people observing the customs exit at the airport can see if your luggage originated in the EU or not. And they have other means. Generally customs is "intelligence" based. They will target individuals they suspect to be smugglers, and leave everyone else alone.