Germany's Foreign Minister Frank-Walter Steinmeier visited both countries last week after a sharp escalation in violence over the disputed region in recent months as war raged in Ukraine.
Although few expect a breakthrough after more than two decades of bloodshed, it is "important to bring the two presidents together, to call on them to work together, to get back to the table to reduce tensions," a French diplomatic source said ahead of the summit.
Armenian separatists backed by Yerevan seized the mountainous region, which is mainly inhabited by ethnic Armenians, from Azerbaijan in a war in the 1990s that left some 30,000 people dead.
Despite years of internationally mediated negotiations since a 1994 ceasefire, the two sides have not yet signed a final peace deal on Karabakh, still internationally recognised as part of Azerbaijan.
Oil-rich Baku, whose military spending exceeds Armenia's entire state budget, has threatened to take back the region by force if negotiations do not yield results.
Armenia — heavily armed by Russia — says it could crush any offensive.
Last August saw a dramatic surge in violence across the countries' border and along the Karabakh frontline as more than 20 troops died in the deadliest clashes since the ceasefire.
Tensions between Azerbaijan and Moscow-allied Armenia have escalated as Russia confronts the West over Ukraine, where government forces are battling pro-Russian separatists.
"What happened in Ukraine has had a direct impact" on the conflict, a source in Hollande's entourage said, adding that Russia's annexation of Crimea "exacerbated the climate".
Azerbaijani analysts say an increasingly assertive Russia is pursuing a divide-and-rule policy and has an interest in keeping the Karabakh conflict in a frozen state to retain its influence over its Soviet-era vassal Caucasian states.
"Moscow holds the keys to the conflict's solution, but is intentionally not using its levers as it has an interest in keeping the status quo, in maintaining its influence over Azerbaijan and, especially, Armenia," Shahin Abbasov, an independent Azerbaijani analyst, told AFP.
Abbasov said that by hosting talks in Paris, Hollande "aims at depriving (Russian President Vladimir) Putin of his role as an exclusive arbiter" in the conflict.
A French diplomat admitted that Hollande will face an uphill battle in his efforts to facilitate the Armenian-Azerbaijani dialogue.
"It would be extremely surprising to have concrete progress. But there is a will from President Hollande to make progress with both parties, to have a dialogue," the diplomat said.
Hollande will hold separate meetings with Azerbaijani President Ilham Aliyev and Armenia's Serzh Sarkisian.
During his talks with Azerbaijan's strongman Hollande will also have to deal with Baku's poor human rights record.
Rights groups say there are dozens of political prisoners in the tightly-controlled Caspian Sea country and the government has clamped down on opponents since Aliyev's re-election to a third term last year.
Prominent rights activist Leyla Yunus and her husband Arif have been held and accused of spying for Armenia — charges denounced by the couple and Human Rights Watch as "bogus".
The ailing 57-year-old activist's three-month pre-trial detention was extended by four months on Friday, despite protests from France and the United States.
The couple's daughter, Dinara Yunusova, has urged Hollande to ask Aliyev to free her parents.
"I would like to ask President Hollande to ask President Aliyev to free my parents and all other pro-democracy activists still in prison in Azerbaijan," she told AFP.