David Cameron said he and recently-elected French president Francois Hollande found “much common ground” when they met in Downing Street today.
On his first presidential visit to the UK, Mr Hollande was greeted with a guard of honour before talks with the Prime Minister.
Their relationship has appeared strained since Mr Cameron refused to meet Mr Hollande while he was running for election.
The Prime Minister has also caused dismay by saying he would "roll out the red carpet" for any French business seeking to flee to Britain to escape higher taxes under the new president.
But at a joint press conference in Number 10, Mr Cameron said they had had "good discussions" on issues ranging across trade, Europe, foreign policy and defence co-operation between the UK and France.
They agreed that measures approved last month by European leaders to shore up the eurozone needed to be implemented "rapidly", Mr Cameron said.
He said they also agreed that the European Commission's proposals to increase Brussels spending by 14 billion euros a year were "unacceptable".
"There will always be areas where we don't agree but we have found much common ground today, not just about European policy today but also how we develop European policy for Britain and for France in the future," the Prime Minister said.
Co-operation between Britain and France at the Channel Tunnel and seaports will "help to guarantee a safe Olympics", Mr Cameron said.
"France is an essential and valued partner of Britain," Mr Cameron said.
"Our economies are closely interwoven, French companies employ 180,000 people across the UK and we export more to France than to China, India, Japan and Turkey combined."
Mr Hollande, speaking through an interpreter, said he and Mr Cameron had the same goal of getting their countries back into economic growth.
"With David Cameron, our relationship has been based on a common intent to put both our countries on the path to growth and recovery."
He acknowledged the two countries had "different positions" on the European Union but that each respected the other's position.
"Britain has no intent to join the eurozone, France would like integration and solidarity within the eurozone - at the same time we understand each other's positions," he said.
"Britain does not wish to slow down or to prevent the eurozone countries from acting, and France within the eurozone does not wish to oblige anyone to join.
"So we should see Europe as having different speeds and each can act at its own speed, while respecting the other countries, and this is the way to build a relationship of trust and a strong relationship."
While the two men agreed the European Commission's current budget proposal was unacceptable, No 10 would not be drawn on suggestions Mr Hollande had backed away from a previous commitment by former president Nicolas Sarkozy to join Britain in opposing any real terms increase.
"We both think the proposal on the table is unacceptable, we both recognise there is a need for restraint, but there is a negotiation which involves 27 countries," the Prime Minister's official spokesman said.