There are no illusions in the corridors of power in Paris that President Jacques Chirac and his outspoken foreign minister, Dominique de Villepin, will be able to repair the damage to their relationship with the Bush administration. By all accounts, Mr. Chirac and President Bush do not particularly like each other, and their administrations deal with each other more out of need than out of friendship.

But the vulnerability of American soldiers in Iraq and the determination by the American military to internationalize the troop presence on the ground have changed the political and diplomatic landscape and raised the possibility that France — and perhaps Washington's other reluctant allies in NATO — could contribute to making peace in Iraq.

Mr. Chirac has ruled out any participation of French troops in a peacemaking or peacekeeping capacity unless there is a United Nations mandate. Senior German officials similarly refuse to consider the deployment of troops without a changed mandate, but as one of them noted last week, "We do not want the American occupation to fail."

In a radio interview last week, Mr. de Villepin argued that only a Security Council resolution handing responsibility for Iraq's security and its political and economic future to the United Nations could secure the peace. "Piecing together a system with what already exists, adding foreign troops to coalition forces, does not seem to us the best way to guarantee security in Iraq," he said.

That said, French military planners are drawing up contingency plans to send troops to Iraq in the unlikely event that France is asked to help fulfill a United Nations mandate, senior French officials said. France could put together a force of 8,000 to 10,000 troops, they added.

France is in effect setting the bar for troop deployment so high that Washington will either not ask for French troops or will refuse to accept French conditions for sending them under a United Nations umbrella, officials suggested.

"In one sense, we were sending a signal to Washington," said one senior French official. "We didn't want to be faced with having to say no." He added, "The French Army would feel humiliated to go to Iraq and be put in the same category as the Poles or the Uruguayans as part of the cleanup team."

After intense questioning at a Senate hearing this month, Defense Secretary Donald H. Rumsfeld told reporters that the United States "would be happy to have troops from a wide variety of countries, including France." In another Senate hearing last week, Gen. Richard B. Myers, chairman of the Joint Chiefs of Staff, said during questioning that "it would be in our best interest" if a NATO force went to Iraq.

Neither France nor Germany is likely to agree to a large NATO role in Iraq as long as the United States is the main occupying power.

"We need to be positive and constructive, and not just snicker in our little corner, saying, `They are in trouble,' " said the former French foreign minister Hubert Védrine in an interview on Europe 1 radio last Friday. "But at the same time, we cannot simply send men in Iraq, in my opinion, to support a policy whose purpose we don't see. So it's about adding troops to the G.I.'s, to do what? We need to talk about the `to do what.' "

But the strategy of setting conditions for possible troop deployment in Iraq could backfire. When Secretary General Kofi Annan of the United Nations asked Mr. Chirac in May to send French troops to lead a peacekeeping force in Congo, Mr. Chirac did not say no but responded with tough conditions. He was said by aides to have been stunned when the conditions were swiftly met.

Complicating any rapprochement with the United States is Mr. Chirac's clinging to his vision of a "multipolar" world in which the United States does not dominate. "We can no longer accept the simple law of the strongest," he said in a prepared statement during a visit to Malaysia last week.

The official Élysée Palace interpreter gave Mr. Chirac's words an even more ominous meaning in English, saying, "We can no longer agree to have the law of the strongest, the law of the jungle," although Mr. Chirac did not use that actual phrase.

What he did say was powerful enough. "What we need is an international structure, an international mechanism to eliminate unilateralism and bring about multilateralism," he said. The goal, he added, is "that nobody feels sidelined, marginalized, humiliated."

At the Group of 8 economic summit in France in June, Mr. Bush assured Mr. Chirac that it was not American policy to be hostile toward France, and he blamed the news media for exaggerating problems.

However, shortly afterward, no American officers above the rank of colonel attended the Paris Air Show in June, and there were no demonstration flights by American warplanes, all on Mr. Rumsfeld's orders.

Mr. Rumsfeld also prevailed upon the Air Force chief of staff, Gen. John P. Jumper, not to invite his French counterpart, Gen. Richard Wolsztynski, to a prestigious September conference — a decision overturned only after bitter complaints through diplomatic channels.

In some areas, relations between the countries are back on track. Tommy G. Thompson, the American secretary of health and human services, who is chairman of the board of Global Fund to Fight AIDS, Tuberculosis and Malaria, was said by French officials to have been particularly gracious at an international AIDS conference in Paris this month.

On the delicate issue of nonproliferation, French officials said cooperation with the Bush administration had been excellent, particularly concerning North Korea's nuclear and missile programs.