It is certainly not an overstatement, and the issue of tax goes far beyond what you may see as an individual (for example, overall labour costs [1]).
France is not an exception in its organisation, in fact its health care system is LESS state-owned than, say, the UK's. But it spends a lot, taxes a lot, and, to compound the issues, is not flexible.
You seem to actually agree that France has problems with its legislation and tax in the rest of your reply...
Edit: The graph that you posted in you reply below is obviously not the same metric. It states it is "general government" spending while I mentioned "public spending". But even so, your graph shows France ahead of Germany and the UK.
[1] https://ec.europa.eu/eurostat/statistics-explained/index.php...