Murray's French Open build-up suffers Bordeaux glitch
Former world number one and three-time Grand Slam title winner Murray was playing his first tournament since suffering an ankle injury in Miami in March.
After winning his opening match on Wednesday to celebrate his 37th birthday in style, the 77th-ranked British star never recovered from slipping 5-0 down to Barrere, a former top 50 player now down at 115 in the world.
In all, Murray was broken six times on his way to a 6-4, 6-2 defeat in just under an hour and a half.
Murray, who will call time on his career later in the year, will now head to the Geneva ATP event next week before a final appearance at the French Open where he was runner-up to Novak Djokovic in 2016.