The 26th-seeded Roddick is 7-10 this season, 0-4 on clay.
Mahut hit more aces than Roddick, 13-8, and broke him seven times, including in the last game on Court Suzanne Lenglen, an arena the American is not fond of.
"I move just horrendously out here. My first step is just so bad on this stuff," Roddick said. "I feel like I'm always shuffling or hopping or not stopping or something. So my footwork on this stuff now is just really bad."
Roddick only once made it as far as the fourth round in 10 trips to Roland Garros, in 2009. He's lost in the first round five times now. And there's a reason the guy never saw success at the French Open the way he did at the U.S. Open (champion), Wimbledon (runner-up three times) or Australian Open (semifinalist four times).
"I just feel like I get exposed too easily out here. I feel like I'm not set on most shots. If you're not set, it's tough to get much of a flow going. When you don't have much of a flow going, it lends itself to sporadic play. It all adds up," Roddick said. "You can't fake it out here. ... It's tough to lie out here."
Back on tour last week after two months away, Roddick was asked a handful of times about his physical state and recovery.
"I'm going to not discuss it. I made a choice. I played. I'm fine. I lost," he said, his expression downcast under a blue baseball hat bearing the logo of his French sponsor.
"Not being confident on something isn't the same as just not being bothered with it. You know, as athletes, we're preconditioned to hope sometimes. Coming into this, I didn't have much to kind of prop myself up on," Roddick said. "But, you know, I played a guy who it's not his favorite surface either, so there was a chance. You just don't know. If everyone pulled out of every tournament when they weren't feeling great or confident, we wouldn't have a lot of fields that were much to write home about. We'd have about four people in most draws."
Mahut lost in the first round eight times in nine previous appearances in Paris. He is best known for losing the longest match in tennis history to John Isner, 70-68 in the fifth set at Wimbledon in the first round in 2010.
Mahut acknowledged the 29-year-old man he faced Sunday "was not the No. 1 Roddick, the No. 1 player in the world that we know."
Still, Roddick did make a bit of a stand, hitting a backhand passing winner down the line to take the third set, then breaking Mahut to open the fourth.
"Then," Roddick would lament, "it fell apart pretty quick."
Now it's on to a happier segment of the season.
"There are a lot of guys who know how to play on clay, and it's just second nature to them," Roddick said. "I feel that way on grass, so hopefully I can turn it around there."
He'll play next at Queen's Club, which starts in London on June 11, then Wimbledon.
After that, he wants to play at the Olympics, which will have tennis on the grass of the All England Club.
And what about his supposed plan to play mixed doubles at the London Games with Serena Williams?
"Ask her. I can't get ahold of her," Roddick replied. "If you see her, ask her for me."
The 2009 U.S. Open champion played with tape on his knee early in the match. The ninth-seeded del Potro then added wrapping after a massage from a trainer following the second set.
"It's a problem when you can't find your balance like you're used to, but I'll use these few days of rest to get better," del Potro said. "If I go on the court, it's because I feel good. I want to continue playing."
Del Potro reached the semifinals at Roland Garros in 2009, but lost to eventual champion Roger Federer in five sets. A few months later, the Argentine defeated Federer in the U.S. Open final.
Tsonga is trying to become the first Frenchman since Yannick Noah in 1983 to win the French Open. His best result at Roland Garros was reaching the fourth round in 2009 and 2010.
He reached the 2008 Australian Open final but lost to Novak Djokovic.
Federer and top-ranked Djokovic will be on court Monday, and Rafael Nadal is to begin his attempt for a record-breaking seventh French Open title Tuesday.
Fabio Fognini of Italy became the first man to advance, beating Adrian Mannarino of France 6-0, 7-5, 6-1. No. 21 Marin Cilic of Croatia was next, defeating Daniel Munoz-De la Nava of Spain 6-4, 6-4, 7-5.
Juan Carlos Ferrero, the 2003 French Open champion, beat Jonathan Dasnieres de Veigy of France 6-1, 6-4, 6-3. The 32-year-old Spaniard is one of 37 men in this year's draw that is 30 or older, an Open era record for Grand Slam tournaments.
"I saw myself in the mirror, and when I walk on the court I don't think about whether I'm younger or older. The only thing I try to do is play well," Ferrero said. "And I'm at Roland Garros, and the idea is to play well today."
The French Open is the only Grand Slam tournament that starts on Sunday. The other three all start on Monday.
Information from The Associated Press was used in this report.