Top seed Novak Djokovic is also safely through to the second round at Roland Garros. The Serb enjoyed a straightforward victory over Poland's Hubert Hurkacz.
In the women's draw, fourth-seeded Kiki Bertens is through after beating France's Pauline Parmentier, while Italian Open finalist Johanna Konta reached the second round for the first time after seeing off German qualifier Antonia Lottner.
However, No. 6 seed Petra Kvitova was forced to withdraw from her first-round match against Sorana Cirstea due to an arm injury.
Former world No. 1 Caroline Wozniacki is also out after suffering a surprise defeat to Russia's Veronika Kudermetova on Court Philippe Chatrier.
Selected Men's Results
(2) Rafael Nadal bt. Yannick Hanfmann 6-2, 6-1, 6-3
(1) Novak Djokovic bt. Hubert Hurkacz 6-4, 6-2, 6-2
Jo-Wilfried Tsonga bt. Peter Gojowczyk 7-6(4), 6-1, 4-6, 6-3
(24) Stanislas Wawrinka bt. Jozef Kovalik 6-1, 6-7 (3), 6-2, 6-3
Selected Women's Results
Veronika Kudermetova bt. (13) Caroline Wozniacki 0-6, 6-3, 6-3
(4) Kiki Bertens bt. Pauline Parmentier 6-3, 6-4
(8) Ashleigh Barty bt. Jessica Pegula 6-3, 6-3
(26) Johanna Konta bt. Antonia Lottner 6-4, 6-4
(12) Anastasija Sevastova bt. Luksika Kumkhum 6-1, 6-4
For a look at all Monday's results, visit RolandGarros.com.
Nadal opened his quest for a 12th French Open by beating Hanfmann in one hour and 57 minutes on Monday.
The win improves his already impressive record on clay, as noted by the ATP Tour:
The defending champion had to save four break points in the opening game but then broke his opponent when the 27-year-old netted a forehand to move 2-0 up.
Nadal cruised through the rest of the match despite managing 11 unforced errors on his fearsome forehand compared to nine winners.
Nadal dropped just six games on his way to victory:
He goes on to play German qualifier Yannick Maden in the second round following Maden's straight-sets victory over Belgium's Kimmer Coppejans.
Djokovic also enjoyed a trouble-free start to his campaign as he continues his bid to hold all four Grand Slam titles at the same time.
The world No.1 had too much for Hurkacz, going on to record his 22nd consecutive win at a Grand Slam:
Hurkacz has enjoyed notable wins over Kei Nishikori and Dominic Thiem in 2019, but Djokovic made light work of the 22-year-old:
Djokovic's win means he will go on to play Henri Laaksonen in the second round Wednesday.