Musetti, 23, who broke into the top 10 for the first time earlier in May, is in sparkling form on clay.
In April he was beaten in the final of the Monte Carlo Masters by Carlos Alcaraz and this month reached the semi-finals of the Madrid Open and Italian Open.
“This month has been incredible. I’ve reached many of my goals,” he said.
“But I think the best is yet to come. I’ve managed to find a way to make the click I needed to step forward in the rankings and in my level.”
He will face either French wildcard Valentin Royer or Colombian lucky loser Daniel Elahi Galan in the second round at Roland Garros.
Elsewhere on Sunday, American 12th seed Tommy Paul came from a set down to beat Dane Elmer Moeller 6-7 (5-7) 6-2 6-3 6-1.
Fellow American Ben Shelton, seeded 13th, needed five sets to overcome Italian Lorenzo Sonego, winning 6-4 4-6 3-6 6-2 6-3 in the night session on Court Philippe Chatrier.
And 15th seed Frances Tiafoe, also from the US, defeated Russian Roman Safiullin 6-4 7-5 6-4.
But two seeds were knocked out of the men’s singles on day one as 32nd seed Alex Michelsen was beaten 6-3 6-2 6-4 by Argentine qualifier Juan Manuel Cerundolo, while another Argentine, Mariano Navone, defeated 28th-seeded American Brandon Nakashima 7-6 (7-2) 4-6 6-1 6-2.
