The Queen has warned that Britain and France cannot afford to be divided while facing threats to their security.
The president and Queen share a joke before dinner
In Paris for a three-day state visit to celebrate 100 years of close links between them, the Queen admitted their relations had not always been smooth.
The countries' recent disagreements have included the war with Iraq.
However at a banquet hosted by President Jacques Chirac, the Queen, speaking in French, said they were "natural 21st century partners".
The monarch, who wore a diamond necklace and Queen Mary tiara, said: "For just as our statesmen and my great grandfather realised 100 years ago.
"We too need to recognise that we cannot let immediate political pressures, however strongly felt on both sides, stand between us in the longer term.
"We are both reminded that neither of our two great nations, nor Europe, nor the wider western alliance, can afford the luxury of short-term division or discord, in the face of the threats to our security and prosperity that now challenge us all."
The Queen's fourth state visit to France is celebrating the centenary of the Entente Cordiale - set up in 1904 to improve diplomatic relations between the two countries.
She spoke of her pride of the role that her great grandfather King Edward VII played in ensuring the historic agreement was signed.
The Queen said she hoped her stay, Mr Chirac's return visit to Britain in the autumn and the Anglo-French alliance celebrations would "contribute to a new
era of Franco-British partnership".
Raising a toast to the president and the people of France, she declared: "Vive la difference, mais vive L'Entente Cordiale."
In his speech, President Chirac spoke of the urgent need for an EU constitution.
"As the European Union prepares to welcome 10 new member states, the new Europe will need to adopt a constitution as soon as possible," he said.
On the fight against terrorism, he described the recent Madrid train bombings as a "tragedy", adding: "Let us present a common front against terrorism.
He continued: "No country can stand apart. No country can act alone."
An affair of the heart
Praising the relationship between Britain and France, he described the Entente Cordiale as an "affair of the heart" that must still be "cultivated".
The President described how the Queen's father and mother, King George VI and the Queen Mother, showed "magnificent courage and solidarity" throughout World War II.
"It is you, the British, who protected the flame of the resistance at the darkest moment in history."
Among the guests was England's winning rugby World Cup captain Martin Johnson, and actresses Kristin Scott Thomas and Charlotte Rampling.
Earlier on Monday the Queen and President Chirac visited the Tomb of the Unknown Soldier at the Arc de Triomphe.