With 90 per cent of the council's agenda "hard-wired" with pre-determined debates there isn't a great deal of room to influence the agenda.
But essentially Mr McCully wants the Security Council as a body to aim higher and be more successful.
"The Security Council has become both the architect and the victim of a culture of low expectations," he said. "We have all been conditioned to expect it to fail - and it almost always meets our expectations."
Mr McCully's plan does not see New Zealand as the peace broker but he wants a leadership role for the Security Council in getting talks started again and offering support.
The window of opportunity is narrowing. The talks with the P5 plus Germany are due to finish any day - and the window is between the end of those talks and the end of the year, before Americans become absorbed in the 2016 presidential elections.
Israel will likely be suspicious of the French initiative. The US is still Israel's strongest ally and has traditionally not seen a role for the Security Council. But relations have cooled since Israeli Prime Minister Benjamin Netanyahu addressed Congress against President Barack Obama's wishes and a veto by the US against a New Zealand resolution from the Security Council is not guaranteed.