After play at Le National was halted for an hour because of a thunderstorm, the Austrian fired a closing 65 for a 13-under par total of 271, leaving him clear of England's James Morrison who finished in second place, on 67 for the day and 274 overall.
Two shots further back came South African Jaco Van Zyl, who had taken a two-stroke lead into the final round, but could only manage a 73 on the day. Former world number one Martin Kaymer of Germany was fourth after shooting 70.
Wiesberger, who had started the final round in third spot, secured the title with a birdie on the 18th hole, his sixth of a flawless round.
Speaking to Sky Sports, the 29-year-old from Vienna said he was "well prepared" for the British Open at St Andrews in a fortnight and "on a high going up to Scotland".
Morrison, Van Zyl and Spaniard Rafael Cabrera-Bello, who finished fifth on five-under, all qualified for The Open. The South African will make his debut at the July 16-19 event.
(Writing By Douglas Beattie; Editing by Mark Meadows and Ken Ferris)
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