> You can move to France with a regular paying job no problem or just a few thousand euros in savings
Unless something has changed dramatically in the last decade this is patently false. Getting an EU work permit was historically very hard with employers having to demonstrate that a position can't be filled by an EU citizen before a non-EU citizen candidate can be considered.
You are correct, however the criteria are a lot more relaxed in Europe comparatively. Most positions in tech, engineering and healthcare are often exempt from labor market tests. Also, there are plenty of options for "entrepreneurs" and self-employed digital nomads, often requiring some savings to prove sufficiency. I live in Portugal, and I believe the amount required when we moved was about 12k. In France, I believe it is closer to 21k (which is basically minimum wage multiplied by 12). Still dramatically easier than 800k in the US.
Indeed those are the rules but on a practical level it seems pretty simple to get a visa if the company had an even reasonably competitive process. Though I moved to Europe 12 years ago (and went through getting work permits twice), maybe it's gotten harder.
Nah it's still very easy. The logic is pretty simple. Europe could really use more talent... and the bar is quite low. Any developer/engineer of any grade will easily get a visa. Any retiree will also easily get a non-work long-term visa with just 1 year worth of minimum wage (around 20k in most of Western Europe) as savings to prove self-sufficiency. So it's extremely easy and almost a non-issue compared to the other side of the pond.
The difference in the US is that it's (comparably) extremely difficult to change status from a temporary visa to a permanent one. Even if you are highly qualified. For example the most common academic visa, the J1, is explicitly a temporary exchange program and you can't have immigrant intent (on application). Most universities won't give out academic H1Bs even though they're cap-free.
In most European countries, once you're in, you can find a way to stay. One exception I can think of is Switzerland, which can be pretty annoying for temporary visas because they don't count for time accrual.
Austria has a pretty good system (RWR) that lets you job seek and is a pathway to permanent residency as a 3rd country citizen. I think there are similar programs in France and Germany.
For example "very highly qualified" in Austria is satisfied by almost anyone with a STEM degree, being under 35 and (amazingly) being an English speaker. If you have that initial visa, companies can hire you without worrying about sponsorship.
You could also use that as a route to the Blue card I think. I wouldn't say the bar is exactly low, but a lot of mobile people are sufficiently educated and are paid enough. As in, a typical European STEM salary would cover it.
But also the grandparent's comment is out of touch. Of course countries want people who are more skilled than local labor, that's the whole point. Aside from the benefit of attracting talent and higher tax revenue, it's much harder for your voters to argue that immigrants are taking your jobs this way.