President Nicolas Sarkozy has said France and Britain have "never been so close", during an historic address to both houses of the UK Parliament.
President Sarkozy spoke for just over 40 minutes
He said he wanted a new "brotherhood", and what brought the countries together was "stronger than what separates us".
His country would "never forget" what Britain did to "free France" during the world wars, he said.
At a later state banquet, the Queen said the countries had a "respectful but competitive relationship".
Mr Sarkozy replied that "friendly rivalry" had ensured "the rise of our mutual peoples".
The UK and France were "two democracies, two lands of freedom, two lands of justice, two lands of solidarity", he told the audience at Windsor Castle.
In his address to Parliament, Mr Sarkozy said France and Britain were stronger side by side, and the world admired the UK's "courage".
Instead of the famed "Entente Cordiale", he said there should now be an "Entente Amicale", marking the friendship of the two nations.
Met at Heathrow by Prince of Wales and Duchess of Cornwall
Joined the Queen and Duke of Edinburgh for state carriage procession to Windsor Castle
Addressed members of both Houses of Parliament
Met leaders of opposition at Buckingham Palace
Windsor Castle state banquet
And France and Britain should work together to tackle the issues of energy, immigration, security and defence, he said.
Both had chosen nuclear power because "they understand this is the energy of the future".
Mr Sarkozy said he knew the EU was a "sensitive issue" for many British people, but he insisted: "Europe needs the UK... we can't build a prosperous, democratic, efficient Europe without the UK.
"Who could imagine Europe would be stronger without British dynamism?
"If we want to change Europe, my dear British friends - and we Frenchmen do wish to change Europe - we need you inside Europe to help us do so, not standing on the outside."
He said the "French-German axis" was an "indispensable driving force" in Europe, but in order to bring its 27 nations together "we need a French-British entente".
He hinted that France might be open to reform of the Common Agricultural Policy - and said the two countries had to work together in the Middle East.
He added that he would propose increasing his country's commitment in Afghanistan at a Nato summit in Bucharest next week.
"If these proposals are accepted, then France will suggest strengthening its presence," he said.
To applause, he said: "We cannot afford to lose Afghanistan. We cannot afford to see the Taleban and Al Qaeda returning to Kabul. Whatever the cost, however difficult the victory, we cannot afford it. We must win."
HAVE YOUR SAY
It's about time the two most influential nations in Europe came together and forged a deeper friendship
Matt, London, UK
Both Mr Sarkozy and Prime Minister Gordon Brown have said they want a new era of closer relations.
Talks on Thursday are expected to cover issues ranging from global finance to Afghanistan.
The two leaders are also expected to unveil new co-operation on illegal immigration and nuclear energy.
Mr Sarkozy is being accompanied by Carla Bruni - the supermodel-turned-singer whom he married last month - and his mother-in-law.
Ms Bruni, a fluent English speaker, will play a prominent role in the high-profile visit, acting as guest of honour at a lunch hosted by Mr Brown's wife Sarah on Thursday.
But as she took centre stage, France's first lady had to suffer the embarrassment of some British newspapers publishing a nude photo of her from 1993.
In an earlier interview with the BBC, President Sarkozy, speaking in French, said he respected Britain's long-held ties with the US, but stressed that this should not interfere with it being at the heart of Europe.
"I perfectly understand that Britain should wish to keep its special relationship with the US, but that doesn't stop Britain from taking its rightful place in Europe," he said.
Lays a wreath at statue of General de Gaulle and meets French war veterans
Visits 10 Downing Street for talks with Gordon Brown
Takes part in UK-France summit at Arsenal's Stadium
Visits Greenwich and presents Dame Ellen MacArthur with the Legion d'Honneur
Attends reception at French embassy for French community in Britain
Attends banquet at the Guildhall hosted by the Lord Mayor
Mr Sarkozy said an example of where the UK and France ties had worked was in the closing down of the controversial Sangatte immigrant camp while he was French home affairs minister.
He said France and Britain, as two nuclear powers, should "work together" as members of the UN Security Council and as partners with "the same vision to reform international institutions"
"Don't you believe that the UK and France are stronger working hand in glove than turning our backs on one another?" he said.
The Sarkozys' 36-hour stay is the first full state visit by a French president for 12 years.
On Thursday, the president will co-host a Franco-British summit at Arsenal Football Club's Emirates stadium, in north London.
The club has strong links with France as its manager Arsene Wenger and a number of its players come from the country.
The president is said by officials in London and Paris to enjoy a "warm" relationship with Mr Brown, whom he has known since they were both finance ministers.
The two leaders are expected to focus on efforts to restore stability to global money markets with a call for banks to be clear about the scale of their bad debts.
They are also expected to suggest permanent representation for Africa on the UN Security Council.