According to Egyptian police and the French Embassy on Sunday, the blast in a traditional market in old Cairo on Thursday evening also killed a French woman, an American man and an unidentified person who police suspect was the bomber.
The Frenchman died on his arrival in France for treatment, a French diplomat said.
Police said 15 people had been detained for questioning about the blast, which wounded 18 other people and had arrested three so far.
The 3kg bomb that exploded near the Khan al-Khalili tourist bazaar was a homemade device, packed with nails, police have said.
Prosecutor-General Mahir Abd al-Wahid has said the investigation revealed that the attack was "an individual act".
Egyptian authorities are investigating whether a suicide bomber carried out the attack.
Egyptian cabinet spokesman Magdi Radi has said the bomb either exploded prematurely or the bomber intended to commit suicide.
Police are questioning 15 people
with regard to Thursday's blast
The government's statements that the attack was a lone act counter a claim of responsibility by a previously unknown group that appeared on the internet on Friday. The claim identified the bomber.
Egyptian officials have sought to limit the potential damage to the tourism industry, the country's top source of foreign exchange.
They have stressed that so far there is no evidence the bomber belonged to a group.
Tourists have returned to Khan al-Khalili, where police have mounted a security presence heavier than usual.
During the 1990s, Muslim insurgents often attacked tourists in a bid to cripple the tourism industry and bring down the government.
The last attack in Cairo was in September 1997, when armed men attacked a bus of German tourists, killing 11.
Two months later, fighters killed 58 tourists at a pharaonic temple in the southern city of Luxor, the last major attack of the 1990s insurgency.
Last October, bomb attacks in two Sinai resorts killed 34 people.