On September 3, 1939 France declared war on Germany. That same month, Gnome et Rhône produced 500 engines. In 1940, it would make a total of 1,000 per month. Unfortunately, after being nationalized in 1937, the aircraft industry was unable to complete its reorganization and could not keep pace with the high production rates demanded by armed conflict.

http://www.snecma.com/en/group/history/1939_60.php

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Was this a major factor in making the French Air Force lose the battle later on? Opinions? Ideas?

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Yes in much the same way the Germans lost the air war due to not enough planes initially. Later on, they were producing planes but not pilots.

Though as far as the french, I also think that their designs were already inferior much like their tanks so they would have lost anyway.

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American by birth, TEXAN by the grace of GOD!