In the manifest information provided to immigration by the airlines, one factor is passengers with no further flights (with that airline)/
With the UK, showing exit from the country, a train ticket on Eurostar for example, would answer their query, being elusive and indefinite would not. Entry into the Schengen area, could prompt the same questions.
As for testing, each country, five of them by my count, will have their own rules, they apply whether you arrive by plane, boat, train, or car. They can also be interpreted to apply going back 10 days or so...so flying to one country, then another, does not wipe thing clean, rules of the country you are arriving from, plus any others you have been in may apply. Plus, per your itinerary above, a London/Paris flight, for example, is not intra-EU, or intra-Schengen. Further, testing requirements for entry are by country, not dependent on whether you are arriving from the EU or not.
All this of course is just talking about entry, once there, other Covid requirements apply. This can include testing (the Netherlands required all non-residents without an EU covid pass to test daily for restaurant and museum entrance), showing proof of vaccination to enter certain places, obtaining a QR code, all variations based what that country decided.