Footage secretly filmed by France 2 TV shows Francoise Olcay selling dinghies and life jackets to migrants hoping to reach the Greek islands.
The UN says 124,000 people reached Greece's shores by sea in the first seven months of 2015.
Ms Olcay said the items would be bought elsewhere if she did not sell them.
Admitting that she was taking part in the trade, she alleged that local Turkish authorities were also involved.
She said others would have taken her place if she stopped selling supplies to the migrants.
The BBC's Hugh Schofield in Paris says that while honorary consuls are not members of the diplomatic corps, the news will be a big embarrassment to the French foreign ministry.
The reporter on France 2 TV who uncovered the news had been investigating where migrants in Bodrum were purchasing their supplies.
His inquiries brought him to a large store, with a French flag flying outside and a sign at the entrance saying "French honorary consul".
Ms Olcay confirmed she was the consul, and that she sold boats to the migrants despite knowing it could lead to disaster.
She told the reporter that it was wrong but everyone was doing it.
Thousands of refugees have used Bodrum as a gateway to fulfil their dream of reaching Europe.
However, correspondents say the number of nightly departures appears to have slightly decreased after Turkish police stepped up patrols in the wake of the death of Alan Kurdi.
The body of the three-year-old was washed up at Bodrum last week, after he drowned along with his mother, four-year-old brother and nine other Syrians as they attempted to sail to the Greek island of Kos.
Images of the boy's body sparked international outrage and highlighted the dangers faced by migrants who make the crossing.
Alan Kurdi death: A Syrian Kurdish family forced to flee
Migrant crisis in maps and charts

Chisako Kakehi was arrested in 2014 and went on trial in Kyoto late last month.
Her lawyers have pleaded not guilty on her behalf, and when her trial began she said only that she would "leave everything" to her defence team.
But in court, asked if she killed her husband, she said there was "no mistake", the Mainichi reported.
The 70-year-old said she committed the crime because her husband was not treating her well financially, and that she obtained the cyanide from a business associate.
"I wasn't given any money after I married him," the Japan Times quoted Ms Kakehi as telling the court on Monday. "I have no intention of hiding the guilt. I will laugh it off and die if I am sentenced to death tomorrow."
Prosecutors say Ms Kakehi targeted the men for their money and poisoned them all with cyanide.
The investigation began when Isao Kakehi, her fourth husband who she reportedly met via a match-making site, died on 28 December 2013, a month after they got married.
A post mortem examination subsequently found traces of cyanide in his body, and investigators then began examining the deaths of other men linked to the pensioner.
She is now on trial for murdering him and two other boyfriends, and the attempted murder and robbery of another boyfriend who later died of cancer.
The men were all aged between 70 and 80 when the alleged crimes took place between 2007-2013.
Ms Kakehi's three other husbands also all died, but she has not been charged in connection with their deaths.
Lawyers for Ms Kakehi say her testimony cannot be trusted, because she has mild dementia.
"Since she is suffering from dementia, she barely remembers things that happened recently let alone the incidents," her team was quoted as saying at the start of the trial, which is expected to continue until November.
Japanese press have dubbed Ms Kakehi a "black widow" - a term derived from the female spider that eats its partner after mating.
In April another Japanese woman, Kanae Kajima, who was convicted of killing three lovers, lost a final appeal against her death sentence at the Supreme Court.
France has suspended its honorary consul in the Turkish port of Bodrum after a TV report showed a shop she owns selling dinghies to migrants.
[NEXT_CONCEPT]
A Japanese pensioner accused of killing three partners and attempting to murder a fourth has told a court that she fatally poisoned her husband.