Comparing a French payslip with another country's
French gross pay carries more contributions than most. The employee pays old-age insurance, the Agirc-Arrco supplementary pension and the CSG and CRDS, and income tax is withheld at source on what is left. The employer then pays a second and larger set of contributions on top of gross, which is why a French gross salary buys less take-home pay than the same figure elsewhere, and why a French employer's budget for a job is well above the gross it offers.
Much of that money pays for things another country's worker buys separately. Health cover and a large part of the pension are inside the deductions. Against an American state the difference is at its widest, because an American net figure has not yet paid for health insurance. Against another European country it is narrower but still real: the countries split the same risks between tax, contributions and private spending in different proportions.
Equal purchasing power, not the exchange rate
The second gross salary on this page is the one that buys the same basket in the other place, derived from official purchasing power parities. Both sides then go through their own payroll rules, and what is left is brought back to one set of prices in the row labelled real take-home. Because both columns begin with the same real income, the difference at the end is the tax and contribution systems and nothing else.
Where the other side is a US state, its price level is chained rather than measured: Eurostat publishes a parity for the United States as a whole, the Bureau of Economic Analysis publishes an index placing each state against the American average, and the state figure is the first scaled by the second. The page notes this above the tables. Against another euro country the exchange rate is one to one, so the whole difference in the second salary is prices.