I've always been an ardent believer in the European program, both for historical reasons (I have French and German grand parents), but also because for all its warts, I believed the EU had a competent bureaucracy, able to go above the pettyness of national politics. French politicians of all side love scapegoating EU for their own failures.
To say that the current situation shattered that conviction would be an understatement. I have no admiration for the Trump administration, but they objectively did almost everything better.
It is also amusing and tragic to see all the core countries (France, Germany, Netherlands, etc.) all doing badly. They cannot frame this as a "cultural" or national failure of specific country like in 2011 at the peak of "Greek" crisis. And 2021 may well be worse than 2020 in number of life affected as populations are tired of various movement constraints, new virus strains coming up, etc.
[edit] my comment comparing US vs the EU was about vaccines, not about the COVID handling in general. For the latter, comparing policies and impact is much harder.
[edit 2] On #deaths, most countries in the EU and Europe in general did not do that much better than the US: France, Spain, Italy, Belgium, the Netherlands all have around ~0.08 - 0.12 % of their population that died from the disease (quite worse for Belgium). And Germany will likely reach that range as well.