> over a 100€ out-of-pocket

My understanding is that you typically pay something like this in the US for a specialist visit even if you have insurance, especially if you haven't already paid the year's deductibles.

You're talking about Paris here, not France. Even 'big' cities like Rennes or Nantes I never had to wait more than a week or two, and in the small city I live in I usually get appointments within a week (but I'm in a high QOL area so we might have a large concentration of specialists), and never out of pocket. But yes, in some areas you will have to drive up to two hours before finding a specialist.

Hey this is not my experience. Getting an appointment for my daughter - in France - was a few weeks wait. But also the whole diagnostic was around 500€, barely touched by the Sécurité Sociale and totally reimbursed by the insurance (mutuelle). This was in a minor city.