American citizen crossing from UK to France

Eurostar is running and definitely open without restrictions to British residents. The UK is outside the Schengen area and the French border police checks passports in London before boarding the train so you cannot hope to fly under the radar and you could very easily be denied entry.

The most important question is whether having spent a mandatory quarantine in the UK is enough to ensure that you are considered as “coming from“ the UK rather than the US. Current rules do not forbid entry based on citizenship or residence and only target people “coming from“ certain countries but do not further define what that means.

I note that there is also a separate measure mandating tests for people coming from the US by air and a test and some other restrictions for people who have stayed in a high-prevalence area in the past month. This would seem to suggest that it is indeed possible to enter France, even if you come from the US (possibly with a travel certificate justifying the purpose of your trip) but that a quarantine might not necessarily exempt you from all restrictions.

When arriving from the UK, there are no restrictions on entry to France. Passport control is done at the St Pancras station in London, but you won't be refused entry on COVID-19 related grounds unless exhibiting symptoms yourself.

You do, however, need to fill out and print the second page of this form (LINK)