The French did not consider it to be a literally impassable area. The French and Belgians had done inter-war year testing and knew full well that tanks could pass through the forest.

The idea that the French thought of the forest as impassable is attributed to the inter-war French General Maxime Waygand, who described it as not requiring defensive fortifications ( to the intensity that the Maginot Line was built), and that if properly defended, the combination of terrain and forest would make the area impassable.

The French were under the impression that it would take the Germans ten days for an armored element to navigate the forest. Especially because they would have to cross a major river where all the bridges were destroyed. They felt the combination of the time and effort involved in moving armor made it an unlikely route of armored attack. As well, they had scouts in villages in the area, which gave them a sense they could see the attack coming.

The French expected, if anything was to be moved through the forest, it would be German light infantry and artillery to move through the forest.

When the Germans attacked, the French scouts were unable to properly communicate what they were seeing to higher headquarters, and the French were unexpectedly attacked by armor (instead of infantry) almost a week earlier than they expected to be physically able. The French high command, without the full reports from scouts were convinced that the reports of German movements in the Ardennes they were receiving were of minor German forces conducting diversions. They sent their limited forces to what they considered more likely routes of attack.

The Germans crossed the rivers especially quickly by deploying pontoons strung along cables to transport their tanks over river crossings. They navigated quickly, with tanks that were able to handle rough terrain better than expected, and in four days had come out of the forest. The communication equipment in their tanks kept the movement organized, and also faster.

The original German plan was drawn up and it called for a huge assessment of Army Group B (8 armored divisions, 2 motorized and 27 infantry) to attack the French/British head-on. This is what the French/British wanted and this is what they planned for when they positioned themselves in Belgium.

Manstein's revision called for Army Group A to filter through the Ardennes in a surprise and overhwelm the weak French defenses on the Allied side of the Ardennes and encircle the Allies in Belgium. Obviously, this is in the past and we know the outcome.

The French were too centered on mastering "conventional" warfare. They expected the Germans to attack their strengths. In my specific opinion, it's quite similar to the way Wolfe was able to exploit Moncalm's weak defense of the Plains of Abraham in 1755.

The biggest single reason for the German success was their implementation of the radio in their tanks and the way they organized their tank units. The conventional French/British/US doctrine called for a bulk of tanks to be infantry support and at the beck and call of infantry. They had no radios and therefore lacked the overarching command/control the German tanks had.

With that all said, this is a really interesting write-up by the US Army Command and General Staff College. It discusses the initial plan and the revision that gave the Germans the advantage. It doesn't really discuss how the Germans got through the Ardennes so much as they were able to exploit poor initial planning by the Allies and the Allies inability to quickly shift focus due to lack of command and control.