It is a little more complex than that.
Within the EU there is also the Schengen area - which the UK is not part of.
Travelling from the UK to the Schengen area means you should complete a Schengen form.
France, though, despite being in the Schengen area does not require this from EU
boats carrying EU citizens arriving from the UK; but Belgium for example does. The challenge then though is finding someone to accept the Schengen form. We have even had official refuse to take them but saying keep it onboard in case we get stopped as some stage.