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USA pension, ss, 401k, IRA will all be taxed first by USA. When you then file France taxes, you get a credit, so pay no French *income* taxes. I assume Spain has the same tax treaty as France, so it shouldn't matter.
I'm still trying to find out about health coverage (cotisation, or ss tax) - if you sign up for this in France, you pay 8% of your taxable income (if you don't, then don't worry about it). It could be either zero, or 8% of all declared income, or anything in between...

So the 8% is on the French income tax number, even though you don't pay it?

So, here's what I found out about social charges / cotisation in France if you r only income is from the US. PUMa is the agency that handles this. You add up all your US income for the year, subtract any deductions (I'm pretty sure, but not 100% sure that this also includes subtracting the baseline allowed by France of ~€9700) and US taxes paid. Then you pay 8% of that total per year in cotisation.
I have zero info on how Spain does it, but if they are anything like France, it will be ridiculously difficult to find out the details.
Note that you don't have to join this, but you do have to have insurance to live in France.

Thanks -

How long have you been in France?
How do you like it?