Gordon Brown, Britain's prime minister, and Sarkozy, both former finance ministers, are said to have developed a good relationship in the past year.
In an interview with the BBC broadcast on Wednesday, Sarkozy said: "I want a new Franco-British brotherhood.
"Often it is our differences that are underlined and underscored... but we enjoy the same music, we like reading the same authors, we have the same enemies throughout the world, we have the same aspiration."
"I would like you to see us as historic allies for the future, as definitive friends. Friends forever. And I would like you to join in the shaping and building of Europe."
After initially gaining high approval ratings, Sarkozy's standing in France has sunk dramatically, especially since he married a former model last month.
The visit is being seen as an opportunity for Sarkozy to present himself in a more "presidential" light.
The French president has sought to improve relations with the US and Britain, which were strained by the US-led invasion of Iraq in 2003, which Chirac resisted.
Some political analysts say he is also reaching out to Britain because he does not get on well with Angela Merkel, the German chancellor.
|Some analysts say Sarkozy is courting Brown|
as he does get on with Angela Merkel [EPA]
Sarkozy said: "Let us try and lay the groundwork for concrete projects. Think of the defence issue: we are the two countries that spend most on defence. Why don't we pool our arms industries so that we spend less money and be more effective?
"On immigration, we shouldn't simply be guarding British borders. That is not our aim in life. Couldn't we better define an immigration policy?
"On the economy, couldn't we try and get the Americans to agree to do something about their dollar?"
Officials said Brown and Sarkozy will urge banks to disclose fully write-offs caused by the global credit crisis.
Banks have written down more than $125bn of assets because of the credit squeeze sparked by low-quality mortgages in the US.
Meanwhile, Sarkozy is eager for French companies to play a role in Britain's plan to build new nuclear power stations to help keep the lights on when North Sea oil and gas runs out.
A French reactor design was one of four given initial approval last week by Britain's nuclear regulators.
On defence, Sarkozy has signalled France might be ready to return to Nato's military structures after a 41-year absence but has made strengthening EU defence capabilities a pre-condition.
Brown's office said the two leaders will also call for reform of the United Nation Security Council to make it more representative, including permanent representation for Africa.