"France can't afford to take back its citizens"
And the UK can afford to take back it's citizens (many of whom are retirees)?
"Would you believe that at he "pole emploi" [...] actively encourages the unemployed to go to the UK."
No, I wouldn't. And given the reputation that the UK is getting regarding how foreigners are treated, the "advice" (if any is given) is likely to be the opposite. Crack open a copy of Ouest-France once in a while or watch the téléjournal.
"For the UK a no-border is obligatory"
For the EU, a barrier between the EU and the non EU is also obligatory, not to mention the lack of any sort of border would make it an easy place for all this uncontrolled immigration that people fear so much. So in essence it's two opposing immovable points of view and since it's the UK who had the brilliant idea of Brexit, it has to be their responsibility to come up with solutions rather than passing the buck and passing the blame like they've been doing for decades.