No, they simply could not due to the lack of raw materials. Adam Tooze, who I have a lot of issues with otherwise, did at least make the point effectively in "Wages of Destruction" that Germany did not use the industrial resources of Europe because of the British blockade of imports, which Europe needed to run its economy. Germany had enough to run her industry, but not enough to make use of all conquered nations' industries. France even had an 'oil famine' that resulted in her demotorizing and going back to horse drawn carriages due to the lack of fuel for her automobiles. Basically the French economy was declining and contributed only a little to the German war effort. What little contribution there was was sabotaged. Daniel Uziel makes that point about Luftwaffe production in "Arming the Luftwaffe".
What the Germans did do effectively was loot the country of anything of use, including industrial machine tools, many of which just sat unused in warehouses, and conscript French labor for German factories where they could be monitored to prevent as much sabotage. Of course so were French PoWs.

Also the French economy was smaller than Germany's so if they could have they would not have had double the resources. They would at best be looking at a 50% increase, but with lots of sabotage. As it was the French did end up contributing a lot of motor vehicles to the German invasion of Russia in 1941, as Germany grabbed whatever it needed from conquered countries, but then ran into supply issues as a single division had 30 different types and brands of trucks that all needed different parts, so once they broke down they were pretty much useless. Also France didn't have a lot of raw materials themselves and were dependent on imports to run their economy in peacetime, so the British blockade pretty much rendered them a burden on the Germans if anything, so diverting resources to them would have been a waste.

Well, "full use" probably not. The Nazis were constrained by their own political system that required them to use people and things inefficiently. But there were systematic efforts to exploit the French people and industrial base.

The Vichy government established the Mandatory Labor Organization, which conscripted Frenchmen into slave labor in Germany. The Germans returned some number of French POW in exchange (although the details are fuzzy in my memory).

The British repeatedly bombed industrial factories near Paris which were used to build trucks and probably other stuff. Of course the French railroads gave up acres of equipment to support the German war effort.

Less well-remembered was the effect of setting the Franc-RM exchange rate in Germany's favor. The Germans could buy French stuff with huge small piles of Marks that were worth large piles of Francs.

This and simple theft allowed a lot of French agricultural goods to feed German troops too.

All in all it added up to quite a bit. It would be interesting to have someone run the numbers to see if the Nazis made a profit when you consider the costs of garrisoning France and so on.