Hollande also met Queen Elizabeth II at Windsor Castle near London on his one-day visit, the socialist leader's first trip to fellow NATO ally and EU heavyweight Britain since he was elected in May.
After talks at Downing Street, Hollande and Cameron stressed their shared ground on foreign policy issues and made light of earlier rows over economic policy and tax.
Hollande in particular joked about "British humour" when asked about the British premier's comment last month that he would "roll out the red carpet" for French residents trying to avoid a planned top tax rate.
That came after the Conservative prime minister apparently snubbed Hollande when he made an election campaign visit to London in February.
"I appreciate humour and, above all, British humour. I was not at all offended, I was very happy to be offered a carpet," Hollande told a joint press conference with Cameron.
Cameron replied: "As for red carpets there was one today for Francois only."
The two leaders also tried to paper over the cracks on the eurozone, a source of strain as Cameron has angered many within the single currency area with repeated calls for them to tackle their debt crisis.
"We can see Europe as having different speeds, with each taking what it wants from the union," Hollande said.
Cameron meanwhile said he wanted there to be "cooperation" between Britain and France -- and welcomed Hollande in French at the start of the press conference.
"There will always be areas where we don't agree, but we've found much common ground today," Cameron said.
"We both want European growth, we both want to stand tall in the world on issues like Syria, or Libya or Iran, we both want to see cooperation between our governments and people, so I'm very happy that we're going to build a strong relationship."
The French leader said Paris and London had "converging views" on Syria, and said they would be pushing Russia and China to back tougher action against President Bashar al-Assad's regime.
Britain's press on Wednesday was unimpressed with the public show of bonhomie, with the high-circulation Daily Mail running with the headline "Hollande hits out at PM's call for French firms to come to UK".
In a similar vein, the Financial Times carried the headline "Hollande clashes with Cameron over tax" while the The Daily Telegraph ran with "Cameron frowns as a French cold front hits No 10".
After his meeting with Cameron Hollande headed to Windsor Castle, west of London, to take tea with the queen during a half-hour meeting.
The 86-year-old monarch, who was wearing a yellow dress, shook hands cordially with the French leader before presenting him with two gifts -- framed and signed portraits of herself and her husband Prince Philip.
"The queen gave him a very warm welcome," a spokesman for the French presidency said.
The warm welcome for Hollande, including a guard of honour at the Foreign Office with lines of soldiers in bearskin hats and red tunics, came after months of frosty relations between the French and British leaders.
Economic issues have been the greatest stumbling block, underlining the ideological differences between Cameron's focus on austerity and Hollande's commitment to boosting growth through spending.
Since Hollande defeated right-winger Nicolas Sarkozy for the presidency in May, he has quickly moved to cement his left-wing credentials, boosting taxes on the rich, vowing to create thousands of public-sector jobs and allowing for slight spending increases.
Cameron continues to urge members of the eurozone -- of which Britain is not a part -- to cut spending and take action to resolve the economic crisis that is severely affecting his country's economy.
He has refused to back the European fiscal discipline pact, which he fears may compromise the City of London's position as Europe's leading financial centre and has regularly voiced his fierce opposition to a financial transactions tax advocated by Paris.
The two leaders largely sidestepped the issues in their press conference, with Hollande also softening his tone on a proposed hike in the levy on foreign-owned second homes, which raised hackles in Britain.