JKW is covered by strict laws in the UK, as per usual, France is 20 years behind the times. There is no legislation regarding treatment/eradication and it is has only recently been considered a problem but not serious enough for a national strategy campaign.
The problem is that if you leave just 1cm of root in the ground, it will grow back. Round-up will shortly be on the banned product list by the way, but injecting each stem with the afore-mentioned (or diesel - very illegal but also very effective) will reduce the activity but you will need to repeat the procedure regularly for the next 5 years. Any foiliage and roots will need to be incinirated, not just dumped over your neighbours wall.
Alas there are no training courses available in France regarding JKW treatment, otherwise I would have done it and made my fortune. There are training programmes available in the UK but guess what, they're not valid in France!
I will contact CEPA (Confederation European Pest Management Associations). I'm not a member, it's too expensive for a "boys club" that need dentures, but there's no harm in asking them the question.
I will keep you informed, but don't expect a rapid response. I will meet with their directors in Paris in November regardless.
In the meantime, as the treatment of JKW comes from local budgets, nobody will touch it. So at the moment, it's all for one and one for all.