The world number one held off the challenge of the home favourite to win 6-4, 7-6 (7-3), 6-4, setting him on his way to a potential 25th Grand Slam title.
Djokovic enjoyed a fairly comfortable first set but had to work hard to win the second as Hubert took a more aggressive approach. He steadied in time for a crucial tie-break though, holding his nerve to secure it.
The Serbian regained control in the final set, sealing the win after a double fault from Hubert to set up a second-round tie against Roberto Carballes Baena.
Data Debrief: Djokovic's title defence off to a good start
Djokovic (367) trails only Roger Federer (369) for Men’s Singles match wins at Grand Slam events in the Open Era, and could overtake him with a strong showing at the French Open.
He is now 72-2 in opening round matches at Grand Slam events, winning his past 69 such matches. Djokovic’s last opening round loss came via retirement at the 2011 US Open against Conor Niland.
World number 15 Monfils would have been expected to breeze through against Carballes Baena, whose lone ATP title came back in February 2018.
But Monfils was trounced in the first set and, despite coming back from a break down to win the second, he could not avoid a shock loss as Carballes Baena reversed a 4-1 deficit in the decisive tie-break on Wednesday.
Carballes Baena's triumph sets up a last-eight clash with eighth seed Federico Delbonis, who beat Thiago Monteiro 7-6 (8-6) 3-6 6-4 at the ATP 250 event in Serbia.
Dusan Lajovic also moved through to the quarters after easing past Jeremy Chardy 6-3 6-4, with Andrej Martin the fifth seed's opponent after upsetting third seed Nikoloz Basilashvili 6-1 4-6 7-6 (7-4).
Elsewhere, top seed Lorenzo Sonego suffered a second-round exit at the Emilia-Romagna Open as Sebastian Korda claimed a surprise win.
Korda entered the tournament with just one clay-court win to his name in 2021 but followed up a first-round success over Andreas Seppi with a 6-1 7-5 defeat of Sonego.
Yoshihito Nishioka is his next opponent after the Japanese saw off Lorenzo Musetti 6-3 6-2.
Jaume Munar and Richard Gasquet also progressed, as did Jan-Lennard Struff, Norbert Gombos, Marco Cecchinato and Tommy Paul.
