The draft text introduced by the US on Friday threatens Iraq with "serious consequences" if it obstructs arms inspections.
France, along with Russia, is seeking to avoid language that could be interpreted as a trigger for military action if weapons inspectors complain about Iraqi co-operation
French Foreign Minister Dominique de Villepin said that, for Paris, the use of force could not be automatic and could only be a last resort.
He was speaking after the Security Council ended two days of discussions without agreement on a draft resolution about Iraq.
'Material breach?'
Mr de Villepin said France wanted a unanimous vote, to send a "firm and clear" message to Iraq.
"We are going to try to work with the Americans on the basis of the text they have proposed," he said.
"If we don't manage that, then we will obviously officially propose our own text," Mr de Villepin added.
The US draft - which is supported by Britain - warns Iraq of "serious consequences" if it hampers arms inspectors in their work.
It also declares Baghdad in "material breach" of UN resolutions.
Correspondents say France and other members of the Security Council are concerned that the "material breach" clause could be interpreted as authorisation for war.
The French text, which has not been formally introduced to the Security Council, deletes "material breach" but includes a reference to "serious consequences".
Veto power
Despite the diplomatic wrangling over the wording of a resolution, Mr de Villepin said the United States had accepted France's wish for a two-step approach on Iraq.
France wants the Security Council to pass a first resolution demanding the return of weapons inspectors to Iraq and then - if Iraq does not cooperate - a second resolution to decide on an appropriate response.
"The Americans have accepted the idea of two stages," the French foreign minister said.
Both Russia and France - as two of the five permanent members of the Security Council - have the power to veto the US draft plan, as does permanent member China.
US President George W Bush, who held talks with Chinese President Jiang Zemin at Mr Bush's ranch in Texas on Friday, urged the Chinese leader to support a tough new UN resolution on disarming Iraq, however Mr Jiang did not give a response.
China has spoken out against a war with Iraq but is expected to abstain on any resolution the council may adopt.
A senior US diplomat, James Cunningham, said the American delegation would consider over the weekend the concerns raised by other members of the council before a vote sometime next week.