The Algerian authorities have indicated that investigating magistrate Marc Trévidic can go to Algeria for a "preparatory meeting" in the second half of November, Hollande told the 18 family members.
It remains what he will be allowed to do, lawyer Patrick Baudouin commented after the meeting.
The families were accompanied by lawyers and Abbot Armand Veilleux, who went to Tibéhrine in 1996 to identify the victims' heads, which were found by a mountain road in May of that year.
The monks from a monestary at Tibéhrine were killed in Algeria in 1996 after being kidnapped by by the Armed Islamic Group (GIA), then locked in a bloody war with the Algerian army.
GIA leader, Jamel Zitouni, claimed responsibility but it has been claimed that he was an Algerian secret service agent.
Different sources, including a former defence attaché at the French embassy in Algiers, French General Françios Buchwalter, believe they were instead killed in a botched operation by the Algerian army.
French investigators have been pursuing the case since 2003 but have met with resistence from Algerian authorities.
In 2009 Trévidic started to take more seriously the theory that the army was responsible for the deaths.
The Tibéhine monks were the subject of acclaimed French film Of Gods and Men, released in 2010.