David Cameron has held talks with French President Nicolas Sarkozy, focused on Afghanistan, the economy and priorities for next week's G8 summit.
The two met in Downing Street after events to mark the anniversary of General de Gaulle's 1940 broadcast to France to resist Nazi occupation.
No 10 said the meeting had been "very warm" and had been an opportunity to "build personal relationships".
Friday's meeting came 24 hours after Mr Cameron's first EU summit as prime minister.
Following their meeting in Paris last month, the BBC's Europe Editor Gavin Hewitt said the two men clearly got on well and were keen to stress both the historical and contemporary ties between the two countries.
At Thursday's summit the UK and France differed over ways to support the eurozone during the current debt crisis afflicting several EU countries and prevent a repeat in the future.
No 10 said the two leaders had discussed "shared priorities" - ahead of the upcoming meetings of both the G8 and G20 groups of industrialised nations in Canada - during a private lunch with their wives in Downing Street.
"In particular there was agreement on the need to step up international efforts on reducing maternal mortality and that this should be a key theme of next week's G8 summit in Canada," a spokesman said.
"The leaders talked through the current state of play in Afghanistan and the global economy ahead of next week's G20 summit."
Speaking earlier at an event in central London to mark former French leader General de Gaulle's London broadcast to his nation to resist Nazi occupation, Mr Cameron praised Mr Sarkozy's leadership and stressed the UK's "shared responsibility" with France.
He said the two men were "committed" to working together to tackle key challenges such as the financial crisis, Afghanistan and climate change.
"Just as our two great countries stood together in the past, so we must stand shoulder to shoulder today," he said.
Mr Cameron has promised to engage with Europe on important issues such as rebuilding economic confidence and growth across Europe but warned that his government will be "on guard" over moves towards further EU integration.
At Thursday's summit, Mr Cameron rejected proposals for new EU powers to scrutinise national budgets before they are presented to MPs and resisted plans for tougher penalties on all EU members for breaching borrowing rules.
The BBC's Political Correspondent Ross Hawkins said the two hoped that by developing a warm relationship in the early stages that it would help when it came to tackling the inevitable disagreements that would surface in future over the direction of Europe.
On a lighter note, No 10 said the two leaders had had an opportunity to "swap notes" on the fortunes of their respective teams at the football World Cup in South Africa.
While France face possible elimination after failing to win either of their first two games, England play their second match - crucial to their continued progress - against Algeria later on Friday.