Well, having lived in France, Eu citizens do better, healthwise, than we did. They changed the rules a few years ago so that you could no longer pay into the urssaf (Nat. Ins. equivalent) until you could prove 5 years residence. This forced a huge number of people into paying thousands of euros for private insurance. A close friend of mine hanged himself from cherry tree outside his front door because he was in such despair. I will forever hold this against French beaurocracy, I went with him to argue his case and we were met with a stone wall. He was a retired Police Inspector (forced to retire at 55). He and his wife owned their home,, paid their dues etc..
For goodness's sake do not believe the lies. The French, for a start, do not obey the rules (I can bear witness to this myself).
France does not admit any right to any benefits until you have been resident for 5 years. European residents here do very well.