Are Apple watches country specific within Europe? I.e. if buy in France but normally resident in UK will there be any issues?

Warranties are not international, and the UK is not international with respect to France.

Also sometimes there are country specific limitations depending on where you purchased the Apple Watch (most likely not in your case, but you should check)

https://www.apple.com/watchos/feature-availability/

There should be no issue with a watch purchased in one EU country (though the UK left the EU, it's still a European country) and used in another EU country.