In an open letter to the French government and Air France chief executive Frédéric Gagey, a crew member named only as Laurent M said homosexuality attracted the death penalty and brutal lashings.
He said "gay stewards from Air France don't want to fly to the death penalty in Iran".
"Sure, our sexuality isn't written on our passports and it doesn't change the way we work as a crew," Laurent M wrote.
"But it is inconceivable to force someone to go to a country where his kind are condemned for who they are."
The petition has already attracted 2368 supporters, a handful shy of its 2500 target.
Air France has not yet indicated whether it will allow gay staff to boycott flights to Iran.
In a statement, the airline pointed out it already flew to countries that had "restrictive legislation regarding homosexuality", and none of those routes had been a problem in the past.
"The cabin crew profession inherently involves working in countries whose cultures and rules are very different from ours," Air France's press office told France 24.
It added "Air France management always strives to ensure that staff members work in the safest environment possible".
Homosexuality is illegal in Iran and same-sex "crimes" are punishable by death and brutal lashings.
Human rights groups have long condemned the government and private sectors for discriminating against LGBT people and putting them at risk of harassment, violence and death.
Homosexuality is treated with such contempt in Iran authorities last year took the bizarre step of outlawing "homosexual haircuts".
Air France will resume flights to Tehran this week after an eight-year hiatus due to strict international sanctions against Iran.
Earlier this month, Air France copped a national backlash for telling its female flight crew they would have to wear pants on flights to Tehran and put on a "loose-fitting jacket and headscarf" before disembarking the plane.
Union groups condemned the airline for "attacking individual freedoms" of staff until it agreed to the opt-out conditions.
Unions have not publicly rallied behind staff in this latest push, however the Unac union, which was part of the action against the dress code, said that cause had been "tackled for the entire aircrew, regardless of their gender or sexual orientation", French news agency Metro reports.
- news.com.au