The reporter, Roxana Saberi, has herself been on a hunger strike for a week. She began refusing food after being sentenced by a court in Iran to eight years in prison for allegedly spying for the United States.
She was convicted after a one-day trial behind closed doors.
Jean-Francois Julliard, the secretary-general of Reporters Without Borders, and a group of the organization's supporters are seated on the sidewalk in front of the Paris offices of Iran Air, the Iranian national airline.
Julliard says Tuesday's action on the Champs Elysees is aimed at mobilizing public opinion in favor of Saberi and other journalists jailed in Iran.
According to Reporters Without Borders, seven journalists and two bloggers are in jail in Iran.
"Roxana Saberi needs to know she is not alone," the organization said in a statement. "We will not abandon her."
Saberi has vowed to remain on a hunger strike until she is freed even though she is "very weak," her father said Monday.
Saberi, who has been on a hunger strike for a week, was convicted more than a week of ago and sentenced to eight years in prison after a one-day trial behind closed doors.
Her parents said they brought her a bouquet of flowers on Sunday - her 32nd birthday - and were able to visit her again in Evin prison on Monday.
"She was already very thin and now she is even thinner," her father, Reza Saberi, told The Associated Press.
Saberi's parents have traveled to Iran from their home in Fargo, North Dakota, in a bid to help win their daughter's release.
According to Reza Saberi, his daughter had been working on a book about the culture and people of Iran, and hoped to finish it and return to the United States this year.
He said he tried to persuade his daughter to end her hunger strike but she refused.
"She vowed to remain on hunger strike" until she is released, he said. "She says that she wants to either die or be free. She does not want to live in the prison, to stay in the prison."
The United States has called the accusations against Roxana Saberi, a dual Iranian-American citizen who was born in the U.S. and grew up in Fargo, baseless and demanded her release.
Iran has released few details about the charges against Saberi.
On Monday, Iran's Foreign Ministry spokesman said Saberi's supporters would be surprised if the judiciary made the evidence against her public.
Hasan Qashqavi didn't elaborate or say what the evidence was against Saberi.
He warned the U.S. not to make judgments or interfere with the case, and stressed that Saberi was tried as an Iranian citizen.
Saberi moved to Iran six years ago and worked as a freelance journalist for news organizations including National Public Radio and the British Broadcasting Corporation.
She received Iranian citizenship because her father was born in Iran.
Saberi's lawyer, Abdolsamad Khorramshahi, appealed the court's ruling on Saturday - days after Iran's judiciary spokesman said an Iranian appeals court would reconsider her verdict, an indication her sentence could be commuted.
Iran's judiciary chief has ordered a full investigation into the case, and President Mahmoud Ahmadinejad has urged Tehran's chief prosecutor to ensure Saberi be allowed a full defense during her appeal.
Saberi was arrested in late January and initially accused of working without press credentials. But earlier this month, an Iranian judge leveled the far more serious allegation of espionage.
The Obama administration has said it is working with Swiss intermediaries who represent U.S. interests in Iran to secure her release.