The campaign against Fabius - led by conservatives including a former representative of the elite Revolutionary Guards, Mojtaba Zolnour - has also criticised his support of Iraq during its war with Iran in the 1980s and his “hard” position during nuclear negotiations.
Ten Iranian MPs - out of 290 - have written to Iranian Foreign Minister Mohammad Javad Zarif asking him to withdraw the invitation for Fabius to come to Tehran, according to news agency ISNA.
Fabius' strategic visit comes after a similar trip by German Economy Minister Sigmar Gabriel, who was the first top Western official to visit the country since world powers and Tehran struck a landmark deal over its controversial nuclear programme after years of negotiations.
Conservative Iranian politicians and media personalities have condemned Fabius, who they blame for sending HIV-infected blood supplies to Iran during his time in office as prime minister in the 1980s.
Infected blood from France’s National Blood Transfusion Centre caused the deaths of hundreds of French people, and an official investigation showed that senior health officials had ordered the continued use of the blood-clotting factor that hemophiliacs need, despite knowing that it had been contaminated.
Even after the supplies were banned, contaminated blood was still exported to countries abroad, including Iran, causing the infection and deaths of hundreds of people.
Fabius, along with former Social Affairs Minister Georgina Dufoix and former Health Minister Edmond Herve, were charged in 1999 with manslaughter. Fabius and Dufoix were later acquitted.
Many of the blood scandal victims’ relatives oppose Fabius’ visit, blaming him for the spread of AIDS in Iran, according to the semiofficial Iranian news agency Fars.
"Fabius is coming to Iran during the Support of Haemophiliacs week and this reminds us about losing some of our compatriots because of imported infected blood. The main cause of this was Fabius," said Zolnour.
He also pointed to French support for now executed dictator Saddam Hussein's Iraq during its 1980-88 war with Iran and the deliveries of Mirage fighters at the time.
"Officials should pay attention to the fact that an enemy is going to enter our country and so our national interests, dignity and power should be preserved," Zolnour said.
The Iranian government has defended Fabius, however.
“It is not in the interest of the country to raise this issue now," Iran’s health minister, Seyed Hassan Hashemi, said of the blood scandal.
Hollande stressed that the visit will be a key test of relations and potential trade. France used to have a strong presence in Iran before the sanctions went into effect, with Peugeot and Renault being major players in the Iranian auto industry and energy giant Total heavily involved in the oil sector.
"The way he (Fabius) will be received is, for us, a test of Iran's behaviour," Hollande told reporters Monday.
Fabius is expected to discuss trade with Iranian leaders, as well as Tehran’s role in supporting peace and security in the Middle East.
Representatives from France's largest employer federation MEDEF are due to visit Iran in September to explore investment opportunities and re-establish commercial ties.
More than 100 representatives from the body travelled to Iran early last year, triggering anger in the US which said it was still too early to do business with Tehran.