Elizabeth, check me and see if I do this fairly and without overly generalizing Europe.
I will assume that the RS statement was a generic European statement and based on that offer:
Allianz does have a list of providers that Allianz will pay direct. The few I have used or researched have all been clinics in the American sense of the word. Outpatient only, even though quite a few are called “hospitals”. The few that I am aware of are excellent private care facilities that provide a level and type and a style of service that will be familiar to Americans. I guess, at least here, they do go a bit beyond a US Clinic in that I have had a few surgical procedures done. But all outpatient.
If the outpatient service does not fit your needs you will probably end up in a national hospital (Allianz may have some private hospitals on their list, but I am not familiar with any). You will be billed for the services you receive. If you aren’t, that’s a mistake and not a policy so don’t count on being one of the mistakes.
France may be wonderful by US standards and expectations, I don’t know; but I do know it has a very good reputation in Europe. I also know that many, many countries have national healthcare facilities that do not reflect what an American patient will be expecting or wanting. To the point of physical and emotional discomfort possibly. If not life threatening you may end up on a waiting list to be seen with a much higher probability than in the US. And I am not talking about obscure 3rd world countries, this is in the EU and UK.
For clarification, there is no “free” healthcare in Europe. In the countries I am familiar with the cost is paid for by those that are employed through a dedicated medical tax on their paycheck. Sort of like an insurance payment deduction in a paycheck in the US … no, exactly the same. While in the US those living near minimum wage will generally pay nothing for healthcare, where I live in Europe the minimum wage earners pay the same tax as the rich folks. I don’t know how this compares across Europe. Probably better in some places, possibly worse in others.