After an even first set that saw two breaks of serve, the Frenchman took control after winning 7-2 in the tiebreak and won the second set 6-1 in just 23 minutes.
Bachinger, who was competing in his first ATP Tour final after defeating world No. 12 Kei Nishikori in the previous round, had three set points in the final game of the opening set but couldn't take advantage.
Simon, who fired 10 aces during the final, battled from 40-0 down to force the decisive tiebreak, before going on to dominate the second set, winning 76 percent of the subsequent points.
It was the third time the former world No. 6 had won the title in Metz, following victories in 2010 and 2013, and was his 14th ATP Tour title overall.