It is difficult to say, as armies are created by the political and strategic situation the country was in. Likely, yes, the US would have failed, because in 1940, the US Army was smaller than Romania's, and wouldn't have had a hope of covering a nation the size of France. It wasn't all that important for the US, they had a large Navy to protect the coasts, the Canadians weren't likely to cause trouble, and the Mexicans weren't that big a military threat.

That said, the causes for the French collapse relate more to the French command structure than to the size of the Army, and I doubt the US would have suffered from similar problems had the US Army been the size of France's. It is my position that the French could have defeated the Germans had two easily rectified issues not existed. The first was the insistence on not using radios, for fear of jamming, interception, or false orders transmitted by the enemy on French frequencies. The UK and Germany had no such compuncitons about using radios, and I haven't really dug into the US side of things, but I suspect from the US's later radio proliferation in the war that the US leaned with the latter two countries. Instead, French units lay about for hours whilst dispatch riders carried written orders around the countryside, often going missing or getting lost. There is even example of the French not conducting an action despite having had the orders verbally read over the telephone (also an unreliable system, when units move), until the courier showed up with the written version. The other problem was that the French commanders often failed to act on their own initiative without orders, or just gave up. Again, this was a problem that the Germans and British did not have.

If you watch my video covering the campaign, and yes, it's 45 minutes long... https://www.youtube.com/watch?v=1E9Da2ge-aM you'll see that there were a number of instances where the French lost out on various 'races' to key positions by a matter of minutes when the French took hours to do anything at all, due mainly to a combination of those two factors. Contrary to common opinion, the idea of a German breakthrough at Sedan had been contemplated, and the French had quite a strong plan for countering it, having done an exercise on just that possibility a month prior. The aforementioned communications and decision lag, however, resulted in the plan being executed terribly and ineffectually, long after it needed to be done.

If you want my hour-long video covering why the French Army had the doctrine and structure it did, this is my video on that topic. https://www.youtube.com/watch?v=ZqoPZK6gyao

To simplify the title question: No.

For the long part: Now people may differ on the specifics of the collapse, but it can be universally agreed upon that World War One crippled Frances effort for World War Two. While Germany looks to have suffered more at first blush, they also had close to a thirty million population advantage in World War One. Their losses mattered less in a long term perspective. Not only that, the French were only fighting on the western front truly, Germany was fighting two fronts, and blew out the Russians in proportional casualties in this war, ending one of the oldest empires of the time.(A fascinating story for another time)

The devastation of French lands had also hardly even been documented, let alone compensated for by the outbreak of the second. German tanks weren’t rolling over defenses, they were rolling over old battlefields that had made tanks needed. Having made peace at all even harmed France eventually, because it made them think that was what winning looked like. The French had long been considered the greatest land power in Europe before this, for good reason, but total war struck mortal blows against it.

While many other problems compounded it, France has been painted rather unfairly for losing a war who’s outcome was decided nearly twenty years prior. Frances population going into WW2 looks like their population going into WW1, and Germany had them doubled. France had spent its youth in the First World War, and would not recover in time.