Elsewhere, Novak Djokovic got his campaign off to a winning start with a 6-3 6-4 6-2 win over Marcel Granollers of Spain.
For good measure, he also won Madrid for a fifth time, ending a two-year seven-match losing streak against Djokovic in the process.
The heavy favourite for the title looked in imperious form as he steamed through the first set in under half an hour, on his way to a 6-1 6-4 6-1 victory.
"Pretty huge disappointment, especially on a surface I really enjoy playing".
Djokovic seemed to get the better of his man after coming up with a clever drop shot for the corner but Granollers refused to give up on the ball and set sail after it.
Agassi has never coached a top player before and Djokovic said he did not expect the American to try to make major changes to his game.
Thanassi Kokkinakis came short in his bid to win his first match at a major in two years.
But a drastic dip in performances, including a shock second-round loss at the Australian Open, left Djokovic scrambling to stop his career from hitting the skids.
Kokkinakis's promising career has been derailed by a shoulder injury that required surgery in December 2015.
After 4 1/2 hours, including a final set that lasted 96 minutes, veteran David Ferrer rallied past Donald Young to reach the second round of the French Open.
The fourth seed is to meet Estonia's Anett Kontaveit for a place in round 3.
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- Australia's Nick Kyrgios beat Germany's Philipp Kohlschreiber 6-3 7-6 (4) 6-3 in the first round.
"It's not about being exhausted, it's about that I had a lot of success on clay, winning three events of four that I played". The 10th-seeded Goffin won 6-2, 6-2, 6-2, sealing the match with an ace.
- The match was halted on Monday due to poor light and rain and play resumed on Tuesday with the scores tied at a set apiece.
The 20-year-old Zverev was one of the outside favorites after impressing on his way to victory at the Italian Open.
But at 31, can he keep the rapid pace which he went though for the first five months of this season? The No. 3 seed kept up his momentum in Paris. "It was not necessarily easy after I played in Geneva until Saturday to get into gear".
One thing Sock is certain about: "I will not", he said, "be in Mallorca next year".
"I just played very bad games on my serve", he admitted after his 6-3 6-4 6-2 win.
Under a hot sun, Djokovic was in a joyful mood on the showcase Philippe Chatrier court. She was broken twice and that will be of concern to her.
Women's 1st rd: Samantha Stosur (Aus) bt Kristina Kucova (Svk) 7-5 6-1, Zhang Shuai (Chn) bt Donna Vekic (Cro) 7-5 6-4, Caroline Wozniacki (Den) bt Jaimee Fourlis (Aus) 6-4 3-6 6-2, Karolina Pliskova (Cze) bt Zheng Saisai (Chn) 7-5 6-2.
Paire has his fans, including 2015 champion Stan Wawrinka, who describes the Frenchman as a "very talented" player who "does a lot of things very well".
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