"Software is expensive because developers are expensive. They are skilled translators–they translate human language into computer language and vice-versa"
I think this is one of the fundamental mistakes that is made by the proponents of AI writing software, and it feels like it comes from a misunderstanding of what software is.
Software is not about language, just as mathematics are not about symbolic notation.
As a point of reference I recently moved back to France from the US where my base salary was ~$190k in California and I now have a base salary of ~100k€ (that's excluding stock and bonus).
I find that my standards of living have not changed much.
There are a few differences (a bit less cash on hand for instance), but all in all it has worked well.
In particular, the protection offered by the French CDI is very valuable in the economy we are in.
Keep in mind that work contracts in the US as generally "at-will" (https://en.wikipedia.org/wiki/At-will_employment), which means that your contract can be terminated at any moment for any reason.
If I were you I would go for 2x in USD and then negociate from there. One thing to consider though is the legality of it, as well as tax implications: will you have a US contract? Are you legally allowed to work in the US?
Regarding taxes you will probably have to declare your income and pay income taxes in both countries, but then receive a "credit d'impôt" for one of the two countries, make sure you get in touch with a tax attorney or a tax expert.