Not entirely true, the Sitzkrieg was pretty much a case of letting the Germans have breathing room.
It's only giving them breathing room if time isn't on your side.
Every day that the war dragged on was a day that the Petite Entente grew stronger and that Germany grew closer to collapse. The French hadn't just sat on their assess since the first world war, they had created an economic defense plan that would let them produce ever greater quantities of newer weapons at a steady and sustainable rate for years. The kept industry crucial men out of the army and could feed themselves indefinitely. France also had
half the gold bullion in the world and could sustain a war for about a year and a half based solely on american imports paid with gold and foreign reserve assets for about a year. And of course they had qualitative superiority over the Germans in general, better planes, better tanks, much better artillery (the weapon that caused half of casualties). Germany on the other hand was going to need to start reducing it's army size in about nine months or else they wouldn't be able to feed themselves while continuing to make the deliveries to the Soviets and Romanians to trade for war vital materials. In absolutely crucial industries like railway rolling stock Germany had a severe deficit as a result of an economy that was drafting resources from industry in a haphazard fashion.
All of these Germans deficiencies disappeared because Gamelin made such a monumental blunder. France collapsed suddenly and Germany suddenly could loot all of Europe. They looted valuables and industrial crucial machines from France. They were free to use military blackmail on Hungary and Romania to get desperately needed agriculture and oil. Rationing was the order of the day in France, the Low countries, the Nordics and eastern Europe and it's this rationing that freed up resources for the Nazi war machine. All of it was made possible because Gamelin didn't leave just another division or two at Sedan to cover his flank.
It's very tragic in the classical sense. Without that one crucial mistake you are looking at a war that would have killed maybe a million men and would have resulted in a democratic victory over Germany with eastern Europe still free. Instead people died by the tens of millions and we got the cold war.