David Cameron has promised to build a "strong relationship" between Britain and France following a meeting with President Francois Hollande.
After talks in Downing Street, he said they agreed that the European Union's budget should not be allowed to expand to "unacceptable" levels.
The prime minister added that he backed moves to establish a banking union among the members of the eurozone.
Mr Hollande said he and Mr Cameron agreed on major international issues.
It is the French president's first visit to London since his election in May, in which he defeated Nicolas Sarkozy.
'Stand tall'The Downing Street discussions focused on the eurozone debt crisis, Anglo-French relations and foreign policy, including the situation in Syria and in Iran.
Mr Cameron said afterwards: "We are trying to build a good and stable relationship. We are both practical, reasonable and rational politicians."
He added: "We both want to stand tall in the world when it comes to issues like Syria and Iran."
Mr Cameron also said: "The eurozone is going to have to integrate more... it will mean there are opportunities for different European countries to have different sorts of relationships [with the EU]... I think that will be possible in the future.
"We are better off within the European Union... but I don't think Britain is happy with its current relationship with the European Union. We need changes and I'm in favour of making those changes and putting them to the peopel to get their consent."
The prime minister said he and Mr Hollande agreed that it was "unacceptable" for the EU to spend £14bn a year more by 2020.
Mr Hollande visited the UK earlier this year when he was socialist candidate for the French presidency, during which he met Labour leader Ed Miliband.
The prime minister was accused by Labour of snubbing Mr Hollande by declining to meet him at the time.
But Mr Hollande said he did not feel he had been snubbed, and that he had not been met by Mr Cameron because he was not in government at the time, adding: "I understand the rules."
Mr Hollande will pay another visit on 30 July, when the London Olympics are under way.
