The answer to the OP is: it depends.
France had a slightly smaller industrial base than Germany and it was much less efficiently arranged for maximising wartime production. So to that extent it was going to start behind, but it had a few major advantages that could tip the industrial war in their favour:
1. They had access to the world market. It was possible for the French to concentrate on manufacturing a limited range of items in massive quantities (similar to what the Soviet Union did) and simply import anything they needed that they were not producing. For example, they Soviet Union virtually stopped producing trucks and locomotives in favour of tanks, and simply acquired the additional items they needed from the world market (U.S.) Germany had to be basically self sufficient in every category of industrial material, so they simply could not specialise in the way the Soviets did and the French could. In addition, the Germans were running on borrowed time in terms of manpower and resources so the French could likely out produce Germany in 1942 simply be having a functioning economy.
2. They had not cannibalised their civilian economy. As other posters have pointed out the German economy was hopelessly overheated and unbalanced in 1939-1940 a fact that was only disguised by the plundering of France and the Low Countries. The German level of industrial production was unsustainable and steel would have to be redistributed to allow the economy to survive. This would inevitably lead to a decrease in armament production.
So, IF France survived past 1940 and IF they were able to optimise their economy and IF the U.S. remained a friendly power willing to sell/lend huge amounts of material then there is a good chance that France could have significantly out produced Germany by 1941/42 in key armaments. If France retained its pre-war economic organisation (or lack thereof), which was certainly possible given the chaotic state of the 3rd Republic's politics, then it would probably never overtake Germany in production (barring the collapse of the German economy, which was more than an outside chance).