Henry posted a 3-point lead over second-round leader Alexandre Rocha under the Modified Stableford scoring system, ending 54 holes with a total of 36 points.
Rocha scored 9 points to end alone in second place with 33 at Montreux Golf and Country Club.
Grabbing sole possession of fourth place at 32 points was John Mallinger, who earned 10 points in Saturday's third round.
Andres Romero also turned in a 10-point round, remaining alone in fourth place with 31 points.
Sharing fifth place at 28 points were Bill Lunde (14), Gary Christian (12) and John Daly (9).
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