I have looked into this now. It was very interesting. But essentially the opposite way around to what you originally posted.
Your initial post said that it would be against human rights to deport someone to France who had an open asylum claim. That was something I was unaware of. Especially as Greece have been doing it for almost a decade. Hence my questions. Your claim turned out to be totally wrong.
What you probably meant to say is that, under the new UK France treaty, the UK cannot send people to France who have an outstanding human rights claim. On the face of it, that appears to be the case. The government say this is not true, although I do not understand their reasoning.