Norrie, 22, stunned John Isner in the previous round but he could not repeat his heroics despite a battling performance in the second set.
Simon didn't look at all troubled as he stormed to victory in the opening set, but Norrie forced him to work for his victory.
As the 'New Musketeers' wind down, what's next for French men's tennis?
The Frenchman will now face either top seed Dominic Thiem or Dusan Lajovic in the final.
It caps a terrific period of preparation for the French Open for Norrie, who will now rise into the top 100 ahead of the tournament.
The Brit has been drawn against ATP Geneva finalist Peter Gojowczyk in the first round.
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