Gen Christophe Gomart told a parliamentary commission in May that a "partner agency" warned of the plot by a Brazilian Islamist militant.
No further details were given.
Gen Gomart made his comments at a commission hearing into last year's attacks in Paris. The transcript of the hearing has just been made public.
Brazil's institutional security cabinet - which oversees the country's information services - told the AFP news agency it had received no information about the threat from the French authorities.
"We were not the source of information and the Brazilian intelligence  agency (ABIN) was not officially informed either of this matter," a spokesman said.
In July, Brazilian Justice Minister Alexandre Moraes said a jihadist attack in Rio during the Olympics was a "possibility" but "not a probability".
About 85,000 security force members including 47,000 policemen and 38,000 soldiers will be on duty to ensure the safety of 10,500 athletes and officials, journalists and tourists from around the world who will be expected to attend the 5-21 August Games.
A spokesman for a special secretariat at Brazil's Justice Ministry - which is spearheading security efforts for the Olympics - said that Brazilian officials and their foreign partners have increasingly been monitoring communications between suspected sympathisers of radical groups.
They have said that the biggest worry is not a co-ordinated attack but a lone actor or group targeting the event.
On Tuesday the federal government said it was releasing additional funding to beef up security ahead of the Olympics.
Brazil's Sports Minister Leonardo Picciani said the armed forces would get an extra $24m (Â£18m) to help them meet security needs.

The 27-year-old Polish man was discovered at a property in Brothertoft Road, Boston, on Saturday.
Three men, who were arrested on Saturday in Larkspur Croft, where a firearm was recovered, were bailed on Monday.
Chf Insp Paul Timmins, of Lincolnshire Police, said the shooting may have been planned.
"The investigation is at an early stage, however the incident does not appear to have been a random offence and I can now confirm that two outstanding suspects have been located and arrested," he said.
The man has been treated at Queen's Medical Centre, Nottingham.

Police said that shortly after 05:00 BST on Sunday they received reports that six windows had been smashed at the property in the Meadow Park area.
Entry had been gained with damage caused to the interior doors.
At 07:00 BST, police received reports that the property had been set alight causing extensive damage downstairs and smoke damage to the rest of the house.
In the intervening period between the two attacks the occupant of the property had left and no-one was injured.
Police said they had attended the scene and helped to secure the premises following the first incident.

The cases involve 165 suspects and more than 100 victims.
A police spokesperson said many cases had "multiple suspects and multiple victims" but there was also a large number involving single suspects.
Last year, 12 men were jailed for their part in the abuse of a single victim in Keighley.
Eleven were jailed at Bradford Crown Court after being convicted of raping the girl from the age of 13 and another man was sentenced for sexual activity with her.
The CSE figures, which were given to the Keighley News and confirmed to the BBC by police, compare with last year's figure of 220 cases.
There were 261 suspects under investigation at the same time in 2016.
A police spokesperson said: "West Yorkshire Police and partners have been proactive in their approach to encourage victims to come forward and reassure them that all reports will be taken seriously.
"We have developed a far greater understanding of CSE than in the past and this has led to rapid action to prioritise resources to improve the identification and prosecution of perpetrators of this abhorrent crime."
France was informed of a planned terror attack on its team at the Olympic Games in Rio de Janeiro, the head of French military intelligence has said.
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Two more arrests have been made after a man was found with gunshot wounds in Lincolnshire.
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Extensive damage has been caused to a house in Newtownards, County Down, during an arson attack.
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A total of 179 cases of child sexual exploitation (CSE) are being investigated in Keighley and Bradford, West Yorkshire Police has said.