Mohammad Moradi, 38, was found in France's Rhone river, which flows through the centre of Lyon, on Monday night, a police official told AFP.
Emergency services were unable to resuscitate him on the riverbank, the official said.
“When you see this, I will be dead,” Mr Moradi said in the video.
“I [have] decided to commit suicide in the Rhone river. It is a challenge to show that we, Iranian people, we are very tired of this situation.
“My suicide is not for personal reasons. The police are attacking people; we have lost a lot of sons and daughters. We have to do something.”
Mr Moradi, a history student who worked in a restaurant, had lived in France with his wife for three years, AFP reported.
The International Community of Iranian Academics wrote on Twitter that “this sad news indicates the traumatising impact of 44 years of an oppressive regime ruling over Iranian people”.
“We wish Mohammad's family peace in this difficult time,” it said.
Mr Moradi's death was followed by an outpouring of support by Iranians, journalists and activists online as a hashtag with his name circulated on social media in Farsi and English.
Prosecutors in Lyon said they had launched a probe to “verify the theory of suicide, in view in particular of the messages posted by the person concerned on social networks announcing his intention” to take his life.
The incident has shocked the city, with a small rally to remember Mr Moradi taking place on the banks of the Rhone on Tuesday.
Mourners placed candles and wreaths on the riverside railings.
“Mohammad Moradi killed himself to make the voice of revolution heard in Iran. Our voice is not carried by western media,” said Timothee Amini of the local Iranian community.
“His heart was beating for Iran; he could no longer bear the regime.”
While the Ukraine conflict was covered “every morning”, one heard “very little about Iran” in the news, Mr Amini said.
Lili Mohadjer said Mr Moradi hoped that “his death would be another element for western media and governments to back the revolution under way in Iran”.
She said his death was “not suicide” but a “sacrifice to gain freedom”.
Mr Moradi said in the video he “could not live peacefully, comfortably here, where he was very well integrated”, while Iranians were being killed, Ms Mohadjer said.
President Ebrahim Raisi said Iran would show “no mercy” towards “hostile” opponents of the country, which has had more than 100 days of protests triggered by the death of Mahsa Amini.
Ms Amini, 22, died in custody after she was arrested and accused of breaching Iran's strict dress code for women.
At least 100 Iranians arrested in more than 100 days of nationwide protests face charges punishable by death, Oslo-based group Iran Human Rights said on Tuesday.
In early December, Iran's top security body gave a toll of more than 200 people killed, including security officers.
At least 14,000 people have been arrested since the nationwide unrest began, the UN said last month.
Italian Foreign Minister Antonio Tajani summoned Iran's ambassador on Tuesday to protest against the “unacceptable” response to the mainly women-led protests.