Russian Pavel Trikhichev was second as he finished on a World Cup podium for the first time and the experienced Italian Peter Fill was third.
It was the second and last combined race of the season and Fill finished as World Cup winner of the category with 140 points.
The discipline, where races feature a downhill leg followed by a slalom leg, has become the poor relation of the World Cup season.
Friday's event was missing a number of both speed and technical specialists, including overall World Cup leader Marcel Hirscher.
Muffat-Jeandet was 27th on the downhill leg, 2.5 seconds adrift of leader Vincent Kriechmayr of Austria while Trikhichev was 29th.
However, Muffat-Jeandet's slalom time of 49.08 seconds was nearly a full second quicker than any of his rivals as he won with a combined time of two minutes 35.29 seconds, 0.96 seconds ahead of Trikhichev.
(Writing by Brian Homewood; Editing by Toby Davis)
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