The Germans had been militarily expanding, preparing and experimenting since 1933. The rest of the world, in short, was not. Not to the same degree; they were still at a peacetime pace.

The industrial capability or booming economy of a country does not necessitate a large and robust army. The US ground forces were only slightly larger than the German's restricted Reichswehr. Politically speaking most countries, France certainly being one of them, were rather keen on avoiding further conflict if possible. A rapid expansion of the military or a serious diversion of government funds to a military all risk serious public backlash if they're seen to be unnecessary or belligerent. Its telling indeed that Germany's initial campaign in 1939 was against a Poland that was unable to fully mobilize and concentrate its forces - signs of (a) being taken by legitimate surprise and (b) avoiding escalating a situation that they hoped could still be resolved peacefully.

I've answered several questions recently that cover this at least in part, so I'll be pulling from them, if you have no objections. As I mentioned, the German military had been undergoing a meteoric expansion and training regime since essentially the day Hitler took power, almost 6 years before the invasion of Poland and 7 years before the Battle of France. I quote:

Versailles limited the German military to 100, 000 men, roughly 10 divisions equivalent, of which 7 were infantry and 3 were cavalry. Hitler's rise to power precipitated a great expansion of the military to upwards of 36 divisions equivalent. The change in size also precipitated an abandonment of the interwar Reichswehr to the Wehrmacht. Military eligibility was expanded to every single German male thereafter, in great contravention of the Treaty of Versailles. The final addition was the 'loyalty oath' - Germans soldiers on 2 August, 1934 (Westwood, pg 7) swore the following oath upon their entry to the Reichswehr:

"I swear by God this holy oath: that I will always be unconditionally obedient to Adolf Hitler, Leader of the German Reich and people, Supreme Commander of the Wehrmacht..."

To meet the demand for rapid expansion of the military, compulsory enlistment was enforced. Men reaching age 20 were contacted and reach through various means - registration lists, professional dockets, university rosters, police records - and alerted. The formation of organizations like the Hitler-Jugend and and a government controlled media prepared following Wehrkriess classes (e.g: Boys of following birth years not yet 20 years old) for compulsory service, rudimentary field training and weapons skills often being learned through the Hitlerjugend. Germans were being trained for military life and discipline well before their eligibility for it, therefore.

Let's think of it this way. If you're a member of a youth program like the HJ in 1933, and you're military eligible in 1939. How much more willing are you to fight, to train, to undergo military discipline? You've been bombarded through your formative years with propaganda, your parents are most likely supportive if not indifferent to the regime, adding a second layer of 'nurture' to your upbringing.

Compare that to potential belligerents:

Its telling that many French formations destroyed during the May 1940 offensive had large numbers of men with the mean age of 45; what most modern military units consider to be the upper limit of your ability to hold a combat position. This manpower crises is directly tied to (a) the slaughter and carnage France suffered in WWI and its direct effects on her population of young, fit men and (b) the French political and military reaction to it. French birth rates were now only beginning to recover, and the expansion of her military pre-war was nowhere near as breathtaking as a re-arming Germany.

My emphasis. What would become the Western Allies didn't really begin to realize that Hitler's desire for land and concessions was insatiable until at least 1938, and didn't begin mobilizing for war until it became clear that Poland was going to be an issue. This means that they only had a matter of months to swiftly mobilize their manpower to a full degree, switch to a more war-oriented economy and accelerate the development of modern doctrines, mechanization, etc. By contrast the Germans had been preparing not only theoretically but practically, sometimes in secret, sometimes in the open, since 1933.

Their ability to prepare a larger percentage of their militarily eligible population for war, over a longer period of time, gave them an undeniable qualitative edge in the years 1939-1941. Irrespective of their production capacities (they did not truly switch to a 'war economy' until 1943). This isn't really to fault the British or French, who valiantly attempted to spare their populations the horrors of war and remain diplomatic until the last possible instant, but rather illustrates Germany's militarization of its culture and its intended effects.

Answers I quoted (and sources therein):

What was training like for German soldiers during World War II?

What was the predominant cause of the French Failure in WW2?

You may also like:

How did the nature of combat contribute to the barbarisation of warfare on the Eastern Front during WWII? - an answer which explains further the doctrinal/political indoctrination of the German military population, and its desired/observable effects.

[WW2] When did the average German realise that the war was lost? - Talking about the Sportspalast Address and Germany's belated switching to a War Economy in 1943.

• [How did Germany's manpower recover for WWII?] (http://www.reddit.com/r/AskHistorians/comments/35z24e/how_did_the_manpower_of_nazi_germany_manage_to/)

• [Why did the Allies fail to limit the size of the Reichswehr?] (https://www.reddit.com/r/AskHistorians/comments/3ajwmh/why_was_the_size_limit_imposed_on_the_reichswehr/)

In short, Germany not only did not suffer as badly as France in WWI, which suffered much worse population wise and saw it's center of industry decimated in the German retreat of 1918, but Germany's population had recovered by the mid 30s to it's pre-war size, despite territorial losses from Versailles. The Germans were on the war path from 1935 onwards, unlike France, and managed to add the populations and industry of the Saarland, Sudetenland, Czechlands and Austria to their own before the battle of France in 1940. The Germans were thus on. Much better footing than France.

EDIT: /u/BritainOpPlsNerf nailed it