Garcia, seeded second, was perhaps feeling the effects of her marathon three-set first-round victory over Timea Babos on Wednesday, as she crashed out 7-5 6-4 to Yulia Putintseva at the WTA 125k series hard-court event.
The Frenchwoman, ranked some 75 spots above Putintseva in the world rankings, had the backing of the home crowd but she put in a disjointed display, dropping serve on five occasions.
Putintseva duly improved her head-to-head record over Garcia to 3-0 and her reward for victory is a quarter-final showdown with another French player in the shape of ninth seed Kristina Mladenovic.
Mladenovic was leading her contest with 2012 runner-up Maryna Zanevska 7-6 (9-7) 3-2, before the latter withdrew from the match.
Schmiedlova, like Garcia, was expected to go far in the tournament but the fifth seed was dumped out by the experienced Francesca Schiavone.
Having lost the first set, Schiavone - the 2010 French Open champion - recovered to win 4-6 6-4 6-3.
Elsewhere, French wildcard Virginie Razzano saw her participation come to an end in a spirited 7-6 (7-2) 6-7 (3-7) 6-1 defeat to Lesia Tsurenko.