France has proposed a forum of ministers from about 20 countries, the EU and the UN but without Israeli or Palestinian representatives, to discuss reviving peace talks before the end of the year.
But, without ruling out cooperation with future attempts, Netanyahu questioned France's right to take such an initiative.
"I told him that the scandalous resolution accepted at Unesco with France's support, that does not recognise the bond of thousands of years between the Jewish people and the Temple Mount, casts a shadow over the impartiality of the entire forum France is trying to convene," he told the weekly Israeli cabinet meeting after meeting Ayrault.
Netanyahu repeated his call for bilateral talks with the Palestinians, while rejecting the Palestinians' condition that Israel stop Jewish settlers from building in the West Bank and East Jerusalem.
"Any other attempt just distances peace and gives Palestinians a means of evading dealing with the root of the conflict, which is not recognising the state of Israel," he said.
Israel attacks Unesco Jerusalem resolution
Israel has already protested about the Unesco motion, adopted last month by the Paris-based UN cultural body, on the Al-Aqsa mosque compound in Jerusalem because it did not mention the Jewish designation of the area, "Temple Mount", and referred to the Jewish place of prayer, the Western Wall Plaza, between inverted commas.
The resolution accuses Israel, which it refers to as the "Occupying Power", of destroying historic structures in the world heritage site and obstructing access to Muslim places of worship.
It also criticises Israel's bombardment and blockade of the Gaza Strip.
France was among 33 countries in the 58-member body to support the resolution.
Netanyahu has already written to French President François Hollande, claiming the motion was a "historic distortion of the truth" and part of a "Palestinian effort to deny Jewish history and to perpetuate the myth of Jewish aggression in the Temple Mount".
Hollande called the French vote a "misunderstanding" in a letter to a French Jewish group and Prime Minister Manuel Valls strongly criticised it.
"This Unesco resolution contains unfortunate, clumsy wording that offends and unquestionably should have been avoidedn as should he vote," he said.
"I want to repeat once again and clearly, with conviciton - France will never deny the Jewish presence and Jewish history in Jerusalem."
Abbas welcomes French move
Abbas and Palestinian foreign policy chief Riyad al-Malki welcomed the French initiative when they met Ayrault in Ramallah.
The meeting came on the day that the Palestinians mark the 68th anniversary of the "nakba" (disaster) of the Palestinian exodus that arose from the creation of the state of Israel.
"The Israeli government was not happy with the French initiative," historian François Géré told RFI. "But the problem is that clearly there has been a major mistake in the French approach by voting this decision by Unesco on the situation of Jerusalem and particularly the mosque compound which, according to Prime Minister Netanyahu, disregards the appellation of Temple Mount.
"This is clearly a pretext to counter the French initiative but it is also very clear that it would have been much better for French diplomacy to avoid any kind of vote in the Unesco on this issue. It has created a real mess."