Yes. Or at least they tried to anyway. Like everywhere else the Germans invaded, productivity in France took a nosedive during the occupation. For instance, the pre-war French aero-industry, which was one of the most productive in the world, became a complete non-factor under German management. I don't have figures in front of me right now (someone summon /u/Georgy_K_Zhukov) but production of things like aircraft engines actually fell by thousands of units per year, a high fraction of total production.

There are many different reasons for this fall in production, likely the most signification were a shortage of food and raw materials.The persistent food shortages that affected most German-occupied areas throughout the war. Most of the French population was not subject to the starvation rations visited upon other occupied peoples, but it certainly made a difference. Similarly, and probably more acutely, Germany was often facing staggering shortages in raw materials, specifically steel and coal. Shortages that were exacerbated by a completely broken system of rations, quotas, and distribution control.

If you want to know more about this, or about the German war economy in general, you should check out "The Wages of Destruction". I can't recommend the book enough.