French President Nicolas Sarkozy has been warmly welcomed in Washington at the start of his first official visit to the US since he was elected.
Mr Sarkozy spoke warmly of French-US relations in a toast to Mr Bush
At a dinner with US President George W Bush at the White House, he said differences over Iraq should not weaken the alliance between the two countries.
Mr Bush agreed, stressing the many areas in which they work together.
The French leader is due to address a joint session of Congress and hold talks with Mr Bush at Mount Vernon.
He will also present the Legion of Honour, France's highest award, to several US citizens.
During the visit, the two presidents are expected to cover topics such as Iraq, Iran's nuclear ambitions, and global warming.
Mr Sarkozy, who was elected in May and spent the afternoon with Mr Bush while on holiday in New England in August, is seen as more pro-American than his predecessor, Jacques Chirac.
The BBC's Richard Lister in Washington says a song of friendship set the tone at the formal dinner at the White House.
Relations between the two countries have been strained since France opposed the US-led invasion of Iraq in 2003, but Mr Sarkozy signalled it should not continue to be an obstacle.
He prompted laughter by saying he had come to show he could be a friend to the US and still win elections in France, underlining his desire to put relations between Washington and Paris on a new footing.
Mr Sarkozy met Mr Bush while on holiday in New England in August
"I came to Washington with a very simple message. I want to reconquer America's heart," he said during a toast to Mr Bush.
"I have come to tell you one thing - that is that France and the United States are friends, we are allies, always and forever."
Mr Sarkozy also paid homage to US troops who had helped liberate France during World War II.
"When we have been together, we have won the hardest fights," he said.
President Bush brushed aside past differences with France and said their countries were working together to solve conflicts around the world.
"French and American troops are helping to defend a young democracy in Afghanistan. Our two nations support the democratic government of Lebanon," he said.
"We agree that reconciliation and democracy in Iraq are vital to the future of the Middle East and our two nations condemn violations of human rights in Darfur, in Burma and around the world."
Correspondents say the Bush administration increasingly sees President Sarkozy as its principal ally in efforts to halt Iran's nuclear programme.
But there will also be some areas of disagreement, they add.
In his address to Congress at 1100 (1600 GMT), Mr Sarkozy is expected to call for the US to do more to combat global warming and international poverty.
Addressing business leaders at the start of his visit, the French leader voiced concern about the weakness of the US dollar.
"A strong economy should have a strong currency. You don't need a dollar too weak," he said.
After visiting Congress, the two leaders will hold talks at Mount Vernon, George Washington's home and estate outside Washington.