Although it is accurate to say that French military opinion was that the Ardennes was a significant barrier to large-scale operations, some important qualifications are in order. Phillipe Petain was on record saying that the Ardennes was impenetrable and Gamelin described the Meuse River as "Europe's best tank obstacle." This however does not mean that the French military completely ruled out any attack through the Ardennes. The French high command estimated that because of the roads and geography, a German attack would likely take nine days to clear the forest and two weeks to reach the Meuse. If a German attack were to materialize in this sector, then the French high command believed they would have ample time to organize an efficient counterattack. Fall Gelb's panzer and mechanized forces proceeded far quicker than the French high command expected, sixty hours to clear the Ardennes and a day to reach the Meuse.

In hindsight, there were many voices within the French military that challenged this complacent attitude in the 1930s. One of the local commanders, Colonel Bourguignon, conducted an exercise that demonstrated tanks could operate far easier within the Ardennes than French conventional wisdom dictated. In 1938, the commander of the French Second Army, General Andre Pretelat, conducted a map exercise that closely resembled Fall Gelb's thrust. Pretelat's estimates of a German attack's speed were only off by a mere three hours. Gamelin accused Pretelat of pessimism and the exercise was kept secret.

It's also worth noting that some in the German high command shared the sentiments of Gamelin. Halder too thought the Meuse could only be reached in nine days at the earliest. Throughout Fall Gelb the German command was torn between two loose factions, the traditionalists and modernizers. The former feared that overextending Panzers without proper infantry support would open up the German thrust to the dangers of an organized counterattack. The modernizers like Guderian favored a Bewegungskrieg (war of movement) and thought that mechanized forces and airpower would make up for the lack of infantry support. Lest we fall into the trap of at type of Calvinist historicism (modernizers are the elect and traditionalist the damned), remember that at various points Fall Gelb took extraordinary risks that could have been disastrous had the Allied forces acted more proactively. At the Battle of Sedan, the official Bundeswehr study of the campaign asserts that the local French commander had everything he needed to stop Guderian except an order to do so.

The German's key advantages were both concentration of forces and operational flexibility. It's important to realize that although the Allies had numerical superiority and a rough technical parity (there's a lot of hair splitting in many of the comments as to how superior one force was over the other), the larger and arguably more important point is that German airpower had effected a numerical superiority over the schwerpunkt. This made it much harder for the French to suddenly shift their airpower over the Ardennes. The Luftwaffe enjoyed a relative proximity to the main bases and were not operating at a distance. German concentration was not limited just in airpower, the I Flak Corps was in full force and prevented Allied airpower from exploiting the gaps in the Luftwaffe air umbrella. Furthermore, the Flak arm proved instrumental in its dual use against French fortifications and Allied tanks (Rommel famously stopped the Cambrai counterattack with his mobile flak units). As Fall Gelb developed, German airpower lost these advantages in concentration of force and proximity to German airfields, and that is when losses started to creep upwards.

Overall, Fall Gelb was successful because it took a calculated risk that payed off handsomely. The Germans offensive played to their strengths, but they were aided considerably by the sluggard French high command.

Sources

Citino, Robert Michael. Death of the Wehrmacht: The German Campaigns of 1942. Lawrence: University Press of Kansas, 2007.

Dildy, Doug, and Peter Dennis. Fall Gelb 1940 (1): Panzer Breakthrough in the West. Oxford: Osprey, 2014. 2014.

Frieser, Karl-Heinz, and John T. Greenwood. The Blitzkrieg legend: the 1940 campaign in the West. Annapolis, Md: Naval Institute Press, 2005.

Above and beyond the technical answers given I would suggest that no one used the word 'impossible' in a literal sense. I've never seen any evidence that that word, or its meaning, were or would have been used. What was certain was that it was considered unlikely, improbable or implausible.

The reasoning for that isnt just the nature of the Ardenne region but that the Allies were mostly assuming the Germans were being defensive, especially midwinter,and that they lacked the resources to mount a campaign of this size and nature. The terrain ADDED to that belief the Ardennes would be quiet over that time, but it certainly was believed impossible per se.

Thus I'd say that I dont believe that it WAS considered impossible in the first place.

I'll look for any sources, but this is kind of a search for negative proof.