Siem started the final round with a big lead, but it had evaporated by the sixth hole.
The German followed with birdies at seven and 11 and took advantage of the struggles of pursuers Mikko Ilonen and David Horsey to regain the advantage en route to his third European Tour title.
Siem finished at 17-under-par 271, three better than Ilonen and Horsey (each of whom fired 3-under 69s) at 14-under.
Pablo Larrazabal corralled sole possession of fourth place at 12-under 276 with a round of 1-under 71 at Golf du Palais Royal.
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