The second seed was solid on serve throughout, not facing a single break point as he prevailed on his fourth match point for his first title of the year.
It was Gasquet's sixth consecutive final in Montpellier, but his second defeat in a row after he was beaten by Germany's Alexander Zverev last year.
Gasquet won the title here in 2013, 2015 and 2016.
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Lucas Pouille à Montpellier
Image credit: Getty Images
Gasquet saved three break points and forced a tiebreak in the first set. Pouille won two points on his opponent's first serve to win it 7-2 and take the lead.
Pouille broke decisively in the seventh game of the second set and did not look back. (Reporting by Julien Pretot; Editing by Clare Lovell)
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