Djokovic, who won the 2016 competition, secured a 6-1 6-4 6-3 victory on Court Suzanne Lenglen in Paris.
He is aiming for his second Grand Slam title of 2019 after winning the Australian Open in January.
The Serb will play unseeded Italian Salvatore Caruso after he knocked out France’s 26th seed Gilles Simon.
Laaksonen was beaten by Sweden’s Mikael Ymer in the third round of qualifying but took his place in the main draw as a ‘lucky loser’ after benefiting from withdrawals.
The Swiss player, ranked 104th in the world, then took advantage of that good fortune by beating Spanish qualifier Pedro Martinez in the opening round to set up a first meeting with 15-time Grand Slam winner Djokovic.
The first set only lasted 23 minutes, but Laaksonen provided more resistance in the second, breaking his opponent’s serve in the sixth game. However, Djokovic twice broke Laaksonen’s serve in consecutive service games to take a two-set lead.
Djokovic then broke again at the beginning of the third set to join Rafael Nadal and Roger Federer in the last 32.