Gordon Brown has announced a series of measures to deepen and strengthen Britain's ties with France saying he wanted an "entente formidable".
The two countries will hold regular bilateral summits - and will vote together for reform of international institutions.
They will also step up cooperation on immigration and defence.
Mr Brown is holding talks with French President Nicolas Sarkozy at Arsenal's football stadium in London.
The Browns earlier gave the Sarkozys a tour of Downing Street. Ms Bruni is attending a charity lunch with Mrs Brown during the summit.
The two women are dining with other wives of senior French and British politicians at Lancaster House, in aid of the White Ribbon Alliance for Safe Motherhood.
Mr Sarkozy and Mr Brown, meanwhile, met Arsenal manager Arsene Wenger at the Emirates Stadium in North London.
Speaking to reporters on the pitch ahead of formal talks, Mr Brown announced a joint British-Franco initiative to help to bring education to 16 million children in Africa.
He also announced a joint initiative between the two governments, the Football Association, Premier League and FIFA, to improve educational opportunities leading up to the 2010 World Cup in South Africa.
Mr Brown said: "We will look to the World Cup in 2010 and the first match in the World Cup to be able to say that millions of children have gained opportunities over the course of the two years leading up to the World Cup."
State banquet
Asked for his comments, Mr Sarkozy, replied in English: "I agree with Gordon."
The two leaders also met members of Arsenal's youth team who greeted the French President in his native tongue.
It is the first state visit by French President for 12 years - but many of the headlines in British newspapers have been grabbed by Ms Bruni.
The supermodel-turned-singer was the centre of attention at a state banquet at Windsor Castle on Wednesday evening, where she chatted with members of the Royal Family.
Before arriving in Downing Street on Thursday morning, Mr Sarkozy and Ms Bruni laid a wreath and observed a minute's silence by a statue of General Charles de Gaulle in Carlton Gardens, off Pall Mall, in central London.
'British dynamism'
In their bilateral talks, Mr Brown and Mr Sarkozy will discuss further measures to tackle illegal immigration including enhanced borders guards at Calais and joint asylum expulsion flights.
They are also expected to speak about measures to tackle global financial instability and announce new co-operation on nuclear energy.
During a historic speech to both houses of the UK Parliament on Wednesday, Mr Sarkozy hailed the historic friendship between Britain and France.
Looking to the future, he said that instead of the famed "Entente Cordiale", there should be an "Entente Amicale", with France and the UK working together on energy, immigration, security and defence.
He also said more "British dynamism" was needed to reform the European Union, hinting that France might be open to changing the Common Agricultural Policy.
He hailed the "exemplary" bilateral efforts to tackle illegal immigration but repeated his call for a common EU immigration "pact" - likely to be a key theme of France's EU Presidency in July.
Mr Sarkozy also proposed increasing his country's commitment in Afghanistan at a Nato summit in Bucharest next week.
Article first appeared on BBC Website|