At a time when fighting terrorism needs a united front, arrogance in Paris and Washington alike is breeding discord, analysts and diplomats say.
The crux is simple: While George W. Bush wants to destroy terrorism, Chirac insists that at best, it can only be contained.
But things have gone beyond the two men's apparent mutual dislike to drag in other leaders.
Turkey, for instance, badly wants to join the European Union. But last month, when Bush endorsed Turkey's ambitions, Chirac essentially told him to mind his own business, saying Europe doesn't tell the United States how to deal with Mexico.
Chirac has enraged eastern European newcomers to the European Union by warning them against supporting the Iraq invasion. He is engaged in a nasty exchange with Ariel Sharon over the Israeli prime minister's claim that France is engulfed in "the wildest anti-Semitism" and that its Jews should get out. And he has angered the Muslim world by championing a ban on schoolgirls' wearing Islamic head scarves at school.
Chirac also sent a message to this month's international AIDS conference in Thailand accusing Washington of tying aid to trade and calling it "tantamount to blackmail."
Such Gallic outbursts are hardly new. But this round appears to represent a sea change.
Iraq is the obvious issue, but underlying it is something much more basic to the French — a sense that their global leadership role, and even their identity, is being submerged in the united 25-nation European superstate they themselves worked to build.
Many believe Chirac, 72 and eligible to run for another term in 2007, is focusing on world affairs to counter growing support for his ambitious young economy minister, Nicolas Sarkozy.
"A very deep gulf is widening across the Atlantic," Jean-Dominique Guiliani of the Robert Schuman Foundation told The Associated Press in Paris.
It's ironic, considering that Chirac is probably the most America-friendly French leader in modern times. Unlike his predecessors, he doesn't mind speaking English in public, and he loves to reminisce about his time in New York as a young man, working as a soda jerk.
Paris and Washington have taken measures to repair their rift, but Anne-Marie Le Gloannec, of the Paris-based Center for International Studies and Research, sees the problem growing.
"Unfortunately, the U.S. administration is extremely arrogant and the French president is extremely arrogant," she said by telephone from Washington, where she is a visiting specialist at the Woodrow Wilson Center.
In fact, she said, Bush and Chirac share similar viewpoints on many issues, but: "They are very much of the same fabric, and each says things in the bluntest way. This makes things dramatic."
Le Gloannec dismisses any notion that France can be an alternative force to America, but believes the two should be talking about "what we all want and how we ought to get there." Events proved Chirac right in insisting on a U.N. mandate to depose Saddam Hussein, she said.
Far from the power centers, this concern is plain in France.
In a column for CBSNews.com, Europe-based CBS News Correspondent Tom Fenton noted that Bush-bashing is good politics in France, and in Europe as a whole.
"Chirac clearly leads the pack as the spokesman for 'Old Europe,'" Fenton wrote.
Roger Casanova, a globe-trotting geologist and former mayor of the Provence village of Ampus, describes himself as staunchly pro-American.
"If Bush had just made a case for removing an evil dictator, we'd have acted in concert, as we did with his father in the first Gulf War," he said. "But he lied to us about the facts and his motives."
A woman buying tomatoes at the Ampus market broke in to say she had just seen Michael Moore's "Fahrenheit 9/11." She said Bush should be tried as a war criminal.
But such sentiments do not necessarily translate into support for Chirac. "He is the consummate opportunist," Casanova said, "and I think people are ready for a change."
Polls put Chirac's approval ratings at just over 50 percent. Television satirists call him "Superliar" and "Superthief," evoking corruption charges from which he is immune as long as he is president.
In other European countries, opinion on Chirac is divided.
Marek Cichocki of the Center for International Relations in Warsaw, told The AP, "Nobody in Poland expects anything good from Chirac anymore," while in Britain, The Sun, a populist tabloid, called him "le Worm."
But another tabloid, the anti-war Mirror, praised France, Germany and Belgium for digging in their heels against the United States.
(c)MMIV, CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report