It's actually very interesting that you should raise this issue, because we're seeing some discomfort on the side of our EU colleagues. This is evolving even as we speak and ever since the Lisbon Treaty in 2009. That division of responsibilities and powers between the EU and member states is still being sorted out. Often during the negotiations, when we try to get some clarity about how this impacts on member states of the EU, they are not even able to respond. That is part of the legal scrub we're going to have to take on at the end of this process.
Generally it's considered to be a mixed agreement, and the EU, as the institution, has a competency. It does have consultations with member states, but ultimately it will be the EU that will sign on behalf of itself and of the 27 member states.