Nope, the level of poverty in Jérôme's graph is absolute (current US poverty line, read the caption). If you increase French per capita GDP to the US level, more Frenchmen will move across the US poverty level.

I before use HDI is variable, because it does take those factors into account

No, it doesn't take them into account. Check the formula. And again, HDI is not a measure of poverty rates.

To repeat the point you avoided, not only is the ratio of poor people much higher in the USA even if we use an absolute income threshold, but the French-US difference is even stronger if we add the virtual value of for-free public services available to the poor.

_{*Lunatic*, n.
One whose delusions are out of fashion.}