At the heart of the "worrying deals", Le Monde says, is the Jalabiya cement works some 150 kilometres north-east of Aleppo that Lafarge bought in 2007.
It went into operation in 2011 and kept up production until 2013, despite growing instability in the region due to the civil war.
In 2013 IS began taking control of towns and roads around the factory.
Le Monde claims to have seen letters sent by Lafarge managers in Syria revealing arrangements that Lafarge made with the jihadist group to continue production until 19 September 2014.
Lafarge bought licences from and paid "taxes" to Islamic State middlemen and oil traders, it alleges, adding that the letters show that Lafarge's Paris headquarters was aware of the arrangements.
In one case Lafarge sent a man named Ahmad Jaloudi on a mission "to get permission from IS to let employees past checkpoints" so as to gain access to its factory for workers and supplies.
In another case a "pass stamped with an IS stamp and endorsed by the [IS] finance chief in the Aleppo region" proves the company had struck a deal with IS to allow for free circulation of its goods, the newspaper reports.
Lafarge, which merged with Swiss company Holcim in 2015, has not commented on the allegations, apart from to say that its absolute priority is ensuring the safety and security of its staff.
"When fighting came closer to the factory, Lafarge's absolute priority was ensuring the safety and security of its staff while the closure of the factory was being studied," the company said.