The French duo were keen to put on a show in front of the home crowd, with Paire winning a point after two ‘tweeners.
But it was Monfils who ultimately prevailed, winning in 87 minutes to set up a third-round meeting with Radu Albot.
Rolex Paris Masters
Paris Masters order of play - Djokovic returns, Ruud, Auger-Aliassime in action
01/11/2021 AT 17:56
Fifth seed Dominic Thiem battled past Milos Raonic in a match which saw just two of 14 break points converted.
Thiem won 7-6(5) 5-7 6-4 and will face Grigor Dimitrov in the next round after the Bulgarian saw off 12th seed David Goffin 7-5 6-3.
Elsewhere, seventh seed Stefanos Tsitsipas beat Taylor Fritz 7-6(5) 6-3 and goes onto face Alex De Minaur, who beat Roberto Bautista Agut 7-6(2) 7-6(1).
Denis Shapovalov fought from a set down to beat Fabio Fognini 3-6 6-3 6-3 and book a showdown with Alexander Zverev.
Stan Wawrinka dug deep to overcome Marin Cilic 7-6(3) 7-6(5), with Christian Garin doing likewise to beat John Isner 7-6(5) 7-6(4).
Rolex Paris Masters
Paris Masters order of play - Murray, Norrie, Evans among ATP stars in action
01/11/2021 AT 08:36
Rolex Paris Masters
When is the Paris Masters? Dates, schedule, draw
27/10/2021 AT 08:37