France has universal care provision, but it isn't free unless you are dependent on benefits, because adults contribute to the state medical scheme according to earnings/income/pension this is the same as the UK - in the UK you pay via NI - the French equivalent "cotisations" - which are a significantly higher proportion of an individual's income which is a key difference and a part of the reason why the NHS and other public services are a mess in the UK. In france if you are working you also pay for a top up private insurance - in the UK many subscribe to BUPA. It isn't the same, but the differences is not to do with "purist state" in the UK - anything but in fact.
Then you pay for GP appointments, and for medication, and recover most of what you paid. If you see a nurse (perhaps to have dressings checked) there's a nursing centre you attend for the care, and you pay for that too! as you say, you recover most of what you have paid....the state sends you a cheque... and the top up insurer if you have one, a small percentage.
@venetianblue i have lived in other countries, yes. And while in the UK I would often go to a private doctor because the NHS gp was so inadequate - it was cheaper for me to pay 45 euro to get some antibiotics than to spend several hours in a nhs surgery waiting only to be told that I would have to go back and wait in a couple of days again if I wanted antibiotics - the argument about whether antibiotics were required aside... but anyway, as we are all agreeing that the NHS is not fit for purpose - my point was that the failure is to do with underfunding and poor management, not anything to do with "purist state". About being free at the point of use - if a non resident uses it they are sent a bill afterwards. It isn't a free for all.