The British number one will play the former world number seven for the first time since their thrilling five-set clash at Wimbledon two years ago, when the Scot emerged victorious.
Gasquet, 23, is currently ranked 68 in the world, but playing on home soil the Frenchman will pose a significant threat to Murray and holds a 2-1 head-to-head record against Murray.
Murray, also 23, Ã‚Â is in the same half of the draw as world number one Roger Federer, who plays Peter Luczak is his first match. Rafael Nadal has been drawn against Gianni Mina.
Murray’s best run at Roland Garros, which gets underway on Sunday,Ã‚Â came last year when he reached the quarter finals where he was eventually defeated by Fernando GonzÃƒÂ¡lez in four sets.
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BIOGRAPHY: Danny Rose
BIOGRAPHY: Antoine Griezmann