What restrictions are there on labor moving between states in the EU? I'm not aware of any at all - witness the large numbers of Poles who now work in the UK (which I admit I rather like).

I don't know about legal restrictions, but I frequently see the claim that people empirically don't move within the EU as much as they move within the US. I'd guess that variability of language/culture probably plays a role...

There are no legal restrictions for most countries; recent entrants to the EU don't get full access to labor markets of most other EU countries immediately. But generally people can move or invest where they like, and EU-wide standards have been established most products and services (so your widget/widgeteria doesn't have to be approved by 22 different regulatory agencies).

There are no internal customs controls in the continental EU; the UK and Ireland reserve an exception, partly due to historical problems with terrorism.

That's probably true - but it is changing fairly rapidly.

I'd certainly be pretty happy to work in some parts of France!

Unrestricted flow of capital, goods and labor was the explicit goal the EU set itself in 1992 when it was founded.

The EU might not be there yet, but they have come a rather long way: I can work and live wherever I want in the EU (I’m from Germany).