I might have this wrong, but last I checked IIRC the deal is your non-EU spouse has a right to live with you (assuming you're an EU national) in any EU country other than your own. She would also have a work permit, should she choose to work. In your own country the local immigration rules apply to your non-EU spouse.

So for a UK citizen with a Taiwanese wife it would be extremely simple (until Brexit of course) to move with her, the "third-country national," to France or Austria or wherever. Whether it's also easy to move to the UK with her, I have no idea... but it's definitely not automatically approved in all EU countries.