The former world No. 2 star improved to a perfect 11-0 on clay this year by handling Argentine Facundo Arguello 6-3, 6-3, 6-1 on a windy Monday at Stade Roland Garros.
The in-form Murray recently captured the first two clay-court titles of his career in Munich and at the Madrid Masters.
The two-time Grand Slam champion has yet to reach a French Open final, as the athletic Brit is a two-time French Open semifinalist, including last year.
Meanwhile, fourth-seeded Tomas Berdych cruised into the second round with a 6-0, 7-5, 6-3 win over Japanese qualifier Yoshihito Nishioka.
The former Wimbledon runner-up Berdych saved all three break points he faced and struck a total of 32 winners. The Czech's best result at Roland Garros came five years ago when he reached the semifinals.
Nishioka had only four winners in the second Grand Slam match of his career. The teenager retired due to an illness in the opening round of last year's U.S. Open.
An upset came when Russian Teymuraz Gabashvili upended 11th-seeded Spaniard Feliciano Lopez 6-3, 7-6 (11-9), 6-3, while 12th-seeded Gilles Simon moved on by overcoming promising fellow Frenchman Lucas Pouille 3-6, 6-1, 6-2, 6-4 and 13th-seeded French favorite Gael Monfils snuck past fellow countryman Edouard Roger-Vasselin 6-2, 6-7 (5-7), 6-1, 7-5.
In other action involving seeds, No. 17 Belgian David Goffin came back to best Serb Filip Krajinovic 3-6, 6-2, 7-6 (7-3), 6-1; No. 18 Spaniard Tommy Robredo fought back to defeat Kazakhstan's Andrey Golubev 3-6, 6-1, 7-5, 6-3; No. 21 Pablo Cuevas of Uruguay overcame Aussie Sam Groth 6-7 (5-7), 6-3, 6-3, 6-3; No. 27 Aussie Bernard Tomic topped Italian Luca Vanni 6-3, 3-6, 6-3, 6-4; No. 28 Italian Fabio Fognini foiled Japan's Tatsuma Ito 6-3, 6-2, 6-2; No. 29 Aussie Nick Kyrgios, slowed by a mid-match nosebleed, humbled Uzbekistan's Denis Istomin 6-3, 6-4, 6-3; and No. 32 Spaniard Fernando Verdasco tackled Taro Daniel 6-3, 6-4, 6-2.
Several other men reached the second round, including Argentine Juan Monaco, last week's Geneva champion Thomaz Bellucci of Brazil, last week's Nice titlist Dominic Thiem of Austria, Colombian Santiago Giraldo, France's Benoit Paire and Czech Radek Stepanek.
The first round is scheduled to conclude on Tuesday, including matches for world No. 1 Novak Djokovic and reigning French Open champ Rafael Nadal. Djokovic will face Finn Jarkko Nieminen, while the sixth-seeded former No. 1 great Nadal will take on Frenchman Quentin Halys.
Djokovic is the reigning Aussie Open and Wimbledon champion who is a two-time French Open runner-up to Nadal, including last year. The Serbian star needs a French Open title to complete a career Grand Slam.
The 14-time Grand Slam titlist Nadal is the all-time leader with nine French Open titles, including five straight here from 2010-14.