Aliyev said he would not meet Prime Minister Nikol Pashinyan in Brussels on December 7 because the Armenian leader demanded that Macron attend the talks.
Pashinyan “agreed to the meeting only on condition” that Macron take part, Aliyev told an international conference in Baku. “That means the meeting will not take place.”
He accused Pashinyan of attempting to “scupper the peace talks.”
Last month Macron and European Council President Charles Michel attended a meeting between Aliyev and Pashinyan in Prague.
On Friday, the Armenian foreign ministry said the meeting in Brussels should have the “same” format.
With Moscow increasingly isolated on the world stage following its February invasion of Ukraine, the EU and the United States have taken a leading role in mediating the Armenia-Azerbaijan peace talks.
On Friday, Kremlin spokesman Dmitry Peskov insisted Moscow was “continuing its work on facilitating” talks between Armenia and Azerbaijan.
Armenia and Azerbaijan have fought two wars — in 2020 and in the 1990s — over Azerbaijan’s Armenian-populated region of Nagorno Karabakh.
The six-week war in 2020 claimed the lives of more than 6,500 troops from both sides and ended with a Russian-brokered ceasefire.
The two countries have recently begun working on a peace treaty under the mediation of the European Union and the United States.
Last month, Aliyev denounced as “unacceptable and biased” a comment from Macron that “Azerbaijan launched a terrible war, with many deaths, (and) atrocious scenes.”
Azerbaijan’s foreign ministry said at the time Baku was “forced to reconsider France’s role in mediating” the peace talks.
Macron also accused Russia of “destabilising” and “seeking to create disorder” in the Caucasus, which Russian President Vladimir Putin said was “unacceptable.”
Last month, Putin’s foreign policy advisor Yuri Ushakov criticised EU and US attempts “to wedge themselves in our work”. The Kremlin sees the Caucasus region as its sphere of influence.
Aliyev and Pashinyan met several times this year in Brussels and Russia’s southern city of Sochi.
Under the Moscow-mediated deal, Armenia ceded swathes of territory it had controlled for decades, and Russia deployed about 2,000 Russian peacekeepers to oversee the fragile truce.
When the Soviet Union collapsed in 1991, ethnic Armenian separatists in Nagorno-Karabakh broke away from Azerbaijan. The ensuing conflict claimed around 30,000 lives.