Tsonga, down at 82 in the ATP rankings after missing seven months of last year because of knee surgery, delighted the home fans with a 7-6(4) 6-1 4-6 6-3 victory.
In-form Benoit Paire, fresh from winning the Lyon title on Saturday, beat Marius Copil of Romania, also in four sets, while Gilles Simon, seeded 26th, overcame Sergiy Stakhovsky.
The standout result, however, was Pierre-Hugues Herbert coming back from two sets down to knock out young Russian 12th seed Daniil Medvedev.
Herbert and Paire face each other next.
"It's 100 percent a French match, which is never easy, but
whatever happens I'm very happy he won in the first round, and I'm very happy to play with him in the second," Paire said.
After missing last year Tsonga, who slumped to 262 in the rankings last November, but won the Montpellier title in February, said it was great to be back, especially with the Roland Garros complex having undergone a radical makeover.
"It's been two years I hadn't played here. It's fantastic and Roland Garros has really changed, so for us players everything has been transformed positively, it's great," said the 34-year-old who trails Nishikori 5-3 in their head-to-head record.
"It's been a long time, and I'm very happy to be back. I'm approaching Roland Garros always in the same manner.
"I'm putting myself under pressure, and I need to revitalise things a bit more and to let my tennis play."
Wildcard Corentin Moutet, 20, also made it through, beating qualifier Alexey Vatutin.
The only French woman to win on Monday was 16-year-old wildcard Diane Parry, who beat Vera Lapko
(Reporting by Martyn Herman; Editing by Toby Davis)
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