[jtheory]

This is how my wife & I moved to France, in 2006; we each got a "Titre de sejour", a 1-year, renewable, long-stay visitor visa.

It's not a regular tourist visa (and in fact if you're in France as a regular visitor/tourist you'll have to leave to apply for a titre de sejour). We needed to prove that we had housing arranged, means to support ourselves (savings plus income coming from outside of France... telework for companies in the US, in my case), and expat medical insurance.

Then we could stay for a year. We renewed this for 5 years and then were automatically upgraded to residence permits (with the right to work in France, actually).

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Edit: somewhere along the way I was checking if some other European countries had similar options -- I remember it wasn't an option in most (it's not allowed in the UK. I think Germany wasn't okay either... forget where else I checked).

Ireland had some options around retiring in Ireland that seemed like they might apply for teleworkers, but I haven't checked into it properly yet.