US Citizen entering France, but via train from other Schengen country - testing requirements?

Requirements are almost always a contingent upon from where you enter France. Presently, there is a rather unusual requirement that:

People coming from Belgium, apart from children under 12, must present proof of full vaccination or a negative result of a PCR or
antigen test taken less than 24 hours prior to the date of arrival.

https://www.diplomatie.gouv.fr/en/coming-to-france/coronavirus-advice-for-foreign-nationals-in-france/

As you will likely need proof of full vaccination to enter into the EU, this requirement is not going to cause you any additional difficulties.

It does not appear at the moment you need to test, but do keep in mind, and for the sake of others reading this, you are obligated to comply with all requirements imposed for countries you have been in for the last 14 days, so if coming from the US requires a test, and you are under that limit, then technically you would have needed to test.

Now, coming by train, or driving across the border, nobody is going to put you in a queue and check your papers (maybe, authorities could meet the train in Paris, especially if you are on Thalys), but if they did, you could face issues if you can not show proof.

My experience last month was that for Germany, the conductor on the Thalys train did remind us we needed to fill out a passenger locator form for Germany. On the Regional train going into Belgium, nothing was said (we may not have even had our tickets checked). The testing in Belgium could be considered voluntary ("should" test day 2 and 7), we could not arrange testing for one, nothing was ever said and it is not tracked. Did not venture into France, but did fly into Amsterdam and spent a night, then left from Amsterdam to the States, but spent the previous night in Antwerp. On the IC train to Schipol from Antwerp, nothing was checked, not even my ticket.

It does not appear at the moment you need to test, but do keep in mind, and for the sake of others reading this, you are obligated to comply with all requirements imposed for countries you have been in for the last 14 days,

Not the case for France. Some countries have the “14 days” built into their requirements etc. France doesn’t.

Some time ago, France did have a 10 or 14 day, qualifying look back window for those originating from red countries and arriving France via a third country. It has been gone for some months (or more).