The break with more traditional surroundings was designed to underline a fresh approach to cross-Channel relations.
Arsene Wenger, Arsenal's manager, is French and the team have several French players.
Sarkozy's UK visit is intended to call for a new, more friendly approach to Franco-British relations, but the French president's first day in London on Wednesday was overshadowed by British tabolid media coverage of his wife Carla Bruni-Sarkozy, a former model.
The Daily Mirror published an old photograph of her naked, below the headline: "Welcome to Great Britain, Madame Sarkozy".
The French president, though, is determined to use his UK visit to project a more statesmanlike image after his ratings at home took a hit following months when his personal life has taken centre-stage.
On Wednesday he attended a state banquet in Windsor Castle's St George's Hall with Queen Elizabeth II.
Brown and his wife Sarah were among 150 guests at the dinner.
It is the first state visit by a French president since Jacques Chirac travelled to the UK in 1996.
Sarkozy's comments on Wednesday that he will be sending more troops to Afghanistan has been criticised by leaders of France's opposition
Segolene Royal, the defeated Socialist candidate in the 2007 presidential elections, said she had been shocked by the statement.
She said: "What surprised me, perhaps shocked me, is that Nicolas Sarkozy talked about France's commitments in Afghanistan before British parliamentarians when there hasn't been the slightest debate before French parliamentarians."
Sarkozy has said he will officially make an offer to send more troops to Afghanistan at a Nato summit in Bucharest starting on Wednesday.
He said the international community could not afford to lose the battle against Taliban fighters there.
"We cannot accept that the Taliban and al-Qaeda return to Kabul," Sarkozy said. "Defeat is not an option, even if victory will be difficult."
At the meeting at Arsenal, Brown and Sarkozy are expected to discuss a number of issues, including France's offer to send more troops to Afghanistan and a call by both countries for greater transparency in world financial markets.
British officials said the two leaders would discuss the global credit crunch that has hit banks round the world and forced Brown to nationalise mortgage lender Northern Rock.
"(They will) call for greater transparency in financial markets and, as a first step, full and immediate disclosure of the scale of write-offs by banks," said one official.
Britain and France have both been hit by recent turmoil caused by the subprime crisis.
Sarkozy and Brown are also expected to talk about a possible joint venture to build a new generation of nuclear-power stations in Britain.
Media reports say the project would help develop a skilled British labour force to work in the power plants which would then work alongside French workers to sell power stations abroad over the next 15 years.
Sarkozy, who returns to France on Thursday evening, is to round off his visit with a speech to bankers and business leaders at London's Guildhall in which he will defend his course of reforms for the French economy.