The summit in Paris follows a visit by German Foreign Minister Frank-Walter Steinmeier to both countries last week after a sharp escalation in violence over the region in recent months as war rages in Ukraine.
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 negotiations since a 1994 ceasefire, the two sides have not yet signed a final peace deal on Karabakh, still internationally recognized as part of Azerbaijan.
Hollande held a first meeting with Azerbaijani President Ilham Aliyev and then with Armenia's Serzh Sarkisian, ahead of three-way talks planned for 1600 GMT followed by dinner.
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.
Although few expect a breakthrough in Paris after more than two decades of bloodshed, a French diplomatic source said 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".
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.