The world number 219, Frenchman Jacquet, felt he could not go on when Murray was leading 7-5 2-0.
Recovering from a ruptured ankle ligament sustained during the Miami Open in March, the British player was making his way back.
On Murray’s 37th birthday, the Bordeaux fans surprised him with a version of ‘Happy Birthday’ at the close of the match, despite his disappointment at finishing early.
After Gregoire Barrere defeated Albert Ramos-Vinolas of Spain 7-6 6-2, he will face the Spanish player in the next round.
Murray made the decision to forego ankle surgery in an effort to speed up his recuperation and return to the field.