Le Pen said the initial count showed her losing to a Socialist in the coal-mining region of northern France by about 100 votes. She suggested she might seek a recount.
Le Pen has sought to bury the party's racist reputation and came in a strong third in presidential elections in April. She wants to abandon the euro currency and stop immigration.
Her 22-year-old niece, party member Marion Marechal-Le Pen, won a seat in southern France. A nationally known lawyer, Gilbert Collard, said he also won a seat for the National Front.