What are the key differences between French citizenship and US citizenship?

With French citizenship, you can live, work, study, own residence and retire in any of the 27 member states of he European Union for unlimited period of time and you don't even require visa for these things. Moreover, France has one of the top national health care systems in the world.
Where as for US, you don't have national health care, there are no international agreements between US and other countries like the one the EU has.