The major European powers will certainly try to rotate the post between them, but I'm not sure that Prime Ministers of the major powers will regard it as a promotion.  Status wise - I would have thought it ranked about equal to the Prime Minister of a medium sized country - e.g. Netherland. Austria, perhaps Poland at a pinch.  This may change over time, but it will take time for the real powers and effectiveness of the role to develop.  

National Governments will guard their prerogatives jealously and major ones will ignore the "President" if it is in their perceived interests to do so.  I see the potential for a lot of confusion between the respective roles of the three "Presidents" and the High Commissioner for foreign affairs.  It doesn't really answer the Kissinger question - who do I ring if I want to talk to Europe...

"It's a mystery to me - the game commences, For the usual fee - plus expenses, Confidential information - it's in my diary..."