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!