Vidadi Isgandarli, who had received asylum in France, was bitterly critical of Azerbaijan's authorities under President Ilham Aliyev and ran a blog and a widely-followed YouTube channel.
The 62-year-old was attacked while sleeping in his apartment in the eastern city of Mulhouse on Sunday by three masked individuals and died of his wounds on Tuesday, the regional prosecutor's office said.
"The violent death of Vidadi Isgandarli must be effectively and promptly investigated," Natalia Nozadze, Amnesty's researcher for the south Caucasus, said in a statement late Wednesday.
"We call on the French authorities to consider all possible motives for his killing, including his criticism of the Azeri president and government, which was the reason for his exile."
The attack came after another France-based exiled critic of the Azerbaijani authorities, Mahammad Mirzali, was punched and stabbed in March 2021 in the western French city of Nantes.
"This is the second time in recent years that an Azerbaijani living in exile in France has been the victim of a knife attack," said Nozadze.
"The French government must ensure effective protection of individuals at risk who are seeking international protection in France," she said.
International focus on the rights record of Azerbaijan -- ruled by Aliyev since the death of his father Heydar in 2003 -- is expected to increase in coming weeks. The gas-rich Central Asian state hosts the COP 29 UN climate change conference in November.
Aliyev, whose vice president is his wife Mehriban Aliyeva, is regularly accused by rights groups of trampling on rights in the ex-Soviet state.
"Opponents of the Aliyev regime have already been attacked in France," French centrist MEP Nathalie Loiseau, a former Europe minister, wrote on X.
"Today one of them is dead. The COP29 in Baku is the COP of shame."
Azerbaijani activists have also urged full investigations into other deaths in Europe of anti-Aliyev activists.*
They include Bayram Mammadov, who Turkish authorities say drowned in Istanbul in 2021, and Huseyn Bakikhanov, who according to Georgian authorities fell from a Tbilisi hotel the same year.