Broady, ranked 78 in the world, failed to take either of her two break points as Parmentier, 30, took the first set.
The Briton, 26, fought hard but was broken when serving to stay in the match in the second set.
France's Parmentier, ranked 113th, beat defending champion Anna Karolina Schmiedlova in straight sets in the first round in Poland.
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British number three Naomi Broady lost 6-4 7-5 to Pauline Parmentier in the second round of the Katowice Open.