"The president said he was convinced the text can be markedly improved so everyone can look upon it favourably," said Mr Chirac's spokeswoman, Catherine Colonna.
"As it stands, the role envisaged for the United Nations is unsatisfactory," she added.
The British-backed draft resolution, presented to the security council 10 days ago, names the UK and America as "occupying powers" in Iraq and gives them control of the country's oil revenues.
It originally relegated the UN to an advisory role, alongside the World Bank and the International Monetary Fund. A revised draft circulated last week beefed up the role of a UN envoy in Iraq.
America would like to see a vote this week and is keen for unanimity, if not a huge majority, to endorse its presence in the region.
But France, Russia and China, all of whom have powers of veto in the UN security council, still have serious reservations, although none is thought likely to use its veto this time.
France is keen to avoid a repeat of the bitter transatlantic row which characterised the talks in the run-up to the war, when France expressed its determination to veto any American and British proposals to secure a UN sanction for the war.
The French foreign minister, Dominique de Villepin, said he was optimistic after speaking to the US secretary of state, Colin Powell, by telephone over the weekend.
"I would like to think that he will take into account the concerns we have expressed," he said.
"In peace, we must find common ground. Let us set aside pride."
The Russian foreign minister, Igor Ivanov, said yesterday that good progress had been made on the draft resolution.
"All sides are in active talks. On some issues we managed to make good progress, but there are disagreements," he said.