Tony Blair and Jacques Chirac have insisted plans for Europe to have its own military capability will not undermine Nato.
President Chirac was given a guard of honour at the Foreign Office
The UK prime minister and French president met in their first summit since their splits over the Iraq war.
President Chirac said US policy on Iraq was now going the right way but was still "somewhat incomplete".
Mr Blair said the pair had agreed to do all they could to combat terrorism in the aftermath of the Turkey bombings.
Later, in an hour-long meeting with Mr Blair, Spanish Prime Minister Jose Maria Aznar said the two countries would "continue working together" against terrorism, which he described as the greatest threat of all.
Other issues on the Anglo-French summit agenda included: the Middle East peace process, asylum, economic growth and climate change.
French Prime Minister Jean-Pierre Raffarin and other French ministers were also involved in talks with their opposite numbers in Downing Street.
Mr Blair said the talks had been "productive" and thanked President Chirac for his "warm sentiments of solidarity" in the wake of last week's terror attacks on the British Consulate and a bank in Istanbul.
Plans for closer European defence policy have alarmed the US, with France keen to have a separate EU military planning headquarters.
There are still thought to be differences between France and Britain over those details.
But Mr Blair said the "practical issues" could be resolved while President Chirac spoke of plans to give "extra efficiency and extra character" to European defence.
The prime minister said Britain did not have to choose between Europe and America and insisted European defence cooperation was not incompatible with Nato.
"It makes to me complete sense in circumstances where Nato is not engaged, for Europe to have the capability and the power to act in the interests of Europe and the wider world," argued Mr Blair.
Jean-Pierre Raffarin was also at the summit
He said Europe had already undertaken military operations in countries such as Macedonia without damaging Nato ties.
That stance was echoed by President Chirac, who said Nato was the "mainstay of European defence".
He continued: "France does not have a problem with Nato...
"However, we believe that there are a number of operations which would be carried out ... by us."
There was a reminder of the two leaders' splits over the Iraq war when President Chirac was asked about the post-conflict situation.
The US policy of transferring sovereignty to the people of Iraq was going in the right direction, he said.
But he went on: "To be quite frank and honest with you, I think it is extending over a somewhat too long a period and it does seem to me a somewhat incomplete policy."
The UN's role should be more clearly specified, he said.
Mr Chirac said the strength of relations between the two countries would be shown in celebrations for next year's centenary of the Entente Cordiale, which calmed Anglo-French relations in a different era.
The Queen will be making a state visit to France from 5-7 April next year to mark the celebrations, with President Chirac making a return trip to Britain.
Mr Blair said he and the Queen had also been invited to take part in next June's 60th anniversary celebrations of the D-Day landings in France.
The talks follow a summit in Le Touquet in February, initially postponed after a row between President Chirac and Mr Blair over the Iraq war.
Farming policy has also caused rifts between the two leaders in the past.
Mr Blair's attempt to reassure critics on European defence was later branded a "deception" by the Conservatives.
Shadow foreign secretary Michael Ancram said: "The breathtaking way in which Tony Blair asserted, with President
Chirac's apparent agreement, that the European defence proposals do not
undermine Nato, is beyond belief.
"The French have for a generation made it a matter of priority that Europe
should provide its own defence outside Nato."