In a letter addressed "Dear George," Chirac -- one of the Republican President's biggest war critics -- extended his best wishes to Bush in the name of France and of himself.
"It is in a spirit of dialogue, esteem and mutual respect that we must continue to develop our cooperation, our shared fight against terrorism and the action we carry together to promote liberty and democracy," the French president wrote.
Chirac told the U.S. president a close transatlantic partnership is essential if the two continents are to meet a variety of challenges confronting them.
Experts are divided over whether transatlantic differences involving the Iraq war and a host of other issues will ease or further widen during a second Bush term.
"We are been staunch allies and friends for a long time," said French Foreign Minister Michel Barnier in an interview on France 2 TV Wednesday night, in which he sought to downplay the transatlantic rift.
While France and the United States disagree on the Iraq war and Europeans and American have two different views of how to build world order, Barnier said "these reasons are reasons to dialogue together" in a climate of mutual respect.