Defeat ended world number 22 Gasquet's 10-match winning streak in Montpellier.
Zverev, who will compete in the doubles final later on Sunday alongside his brother Mischa, had beaten much-fancied second seed Jo-Wilfried Tsonga in his semi final.
Gasquet saw off compatriot Benoit Paire to reach the final.
(Reporting by Ed Dove)
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