Whilst not a signatory to the Schengan the UK and France are working at frontiers WITHIN the EU within the Schengan framework.
Also The Eurostar operates under very special acts of Parliament !
Remember please that FREE an un-restricted travel within the EU is enshrined in the various treaties and actually the UK is acting largely alone by wanting to count people OUT of the country !
France does not need to run any formal frontier checks on ANY EU citizen be they Schengan or not - You just need to be carrying a EU approved ID card
(No need for a full passport and you know the UK had a very nice and easy travel document that could have met with this requirement - The old annual UK visitor visa- Cancelled without a suitable replacement because the gov want more revenue till such time we have that national ID card !)
The US pre-clearance issue whilst visually similar would be a whole differing ball game for the UK !