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 summits and step up co-operation on immigration, defence and the economy.
French President Nicolas Sarkozy also hailed a new era of friendship - but said Britain still needed to play a fuller role in the EU.
The two spoke at a media conference at Arsenal's football ground in London.
Britain and France issued a 36-page joint communique setting out areas where they plan to work more closely together, including:
- Reforming the G8 to include more members and UN Security Council to include "permanent representation" for Africa, and "permanent membership" for Germany, India, Brazil and Japan
- Promoting peace in Darfur and pushing for greater human rights in Burma
- New counter-terrorism measures, including scanning traffic at the Channel Tunnel to combat "nuclear terrorism"
- Greater pooling of military resources, including more cash for joint research and development
- Tightening up border controls at Calais, including fencing around the port
- Cooperating on a new generation of nuclear power plants by sharing information on safety, security and waste disposal
The communique was particularly detailed about planned cooperation on defence projects - including "a joint industrial strategy for complex weapons" and co-operation to "develop European military capabilities".
At their press conference, Mr Brown said Britain and France shared the same vision for the future of Europe.
"Our two countries are at the heart of what we want to be an outward looking and globally focused Europe.
"We both favour a strong relationship with our American partners. We agree that only by working together can we confront the challenges we face from terrorism, from climate change, poverty, disease and failed states."
He added: "We believe that working together, France and Britain can be an even greater force for good in the world of tomorrow and so, if you like, this will be an entente formidable as well."
Mr Brown also called for greater international co-operation to prevent a repeat of the credit crunch, saying he had agreed a "co-ordinated approach" with France to improve transparency and stability.
Mr Sarkozy said that although he and Mr Brown were at different ends of the spectrum politically - they were "on the same wavelength" personally.
Asked if the closeness with France demonstrated during Mr Sarkozy's visit would last, Mr Sarkozy joked: "It is more than a one-night stand, we will go into the next day breakfast."
He also said he had been "deeply moved" by the reception his new wife Carla Bruni had received in the UK following negative coverage of their relationship in the French media.
"I am proud that people have seen her for what she really is and that there is a sense of justice," he said.
The French President also repeated his call for Britain to play a fuller role in the EU, on issues such as immigration and the Lisbon treaty, rather than "being on the sidelines".
"We need the British to get Europe moving," he told reporters at a joint press conference.
Gordon Brown and wife Sarah had earlier given President Sarkozy and Ms Bruni a tour of Downing Street.
The leaders' wives then attended and spoke at a dinner 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.
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.
After the meeting with the Browns the French president and his wife headed by boat along the Thames to Greenwich as their 36-hour visit approached an end.
On Thursday evening they attended a banquet, hosted by the Duke and Duchess of Gloucester, at the Guildhall in London, at which the president inspected a Guard of Honour.