Tsonga will face Germany's Cedrik-Marcel Stebbe for a place in the third round.
"Against such a player, you feel, okay, let's wait for the storm to be over and in half an hour I'll see what's going on," said Tsonga of his opponent, who was the 2009 Wimbledon junior champion, but was making his debut in Paris.
Tsonga has never got beyond the fourth round at the French Open and insisted there is no pressure on him to deliver a first home champion since Yannick Noah 29 years ago.
"I have nothing to lose. I have no points to lose. Last time I lost in the third round. If I was to lose in the first round, I would lose 90 points, so that's peanuts," he said.
"It's not my favourite surface at the moment. Trust me, I'll have more pressure at Wimbledon."
Tsonga reached the semi-finals at Wimbledon last year, knocking out Roger Federer in the last eight in five sets before losing to eventual champion Novak Djokovic.
Tsonga overcomes jitters to make French Open last 64
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