If ones defenses seems impenetrable remember the French Maginot line and the German attack strategy:

From Wickipedia:

"The French established the fortification to provide time for their army to mobilize in the event of attack and/or to entice Germany to attack neutral Belgium to avoid a direct assault on the line. The success of static, defensive combat in World War I was a key influence on French thinking. The fortification system successfully dissuaded a direct attack. However, it was an ineffective strategic gambit, as the Germans eventually flanked the line, and proceeded unobstructed. [1]"

Flank the Bastards !

Tut tut...Of course the Germans flanked the line...As they were supposed to do...BUT nobody foresaw they'd roll their Panzers through the Ardennes, which allowed them to take the Allied forces between pincers. It would not have been politically acceptable to fortify France's entire northern border, essentially signaling that France would not fight beside Belgium, and what's more, it would probably have been ruinously expensive. The Maginot line was expensive enough as it was, but it's purpose was to free French forces from having to defend in two places at once. If only it had been just a little longer...

Even if it had been longer it still would have failed. That style of warfare was past its time. For sure they would have held out longer and perhaps given the English more of a chance to get their forces established but when it comes down to it the French were still war weary from having lost an entire generation to world war 1. Not that i blame them, but the French were willing to be occupied rather than lose another generation.

I was addressing this peculiar misconception that the Maginot Line was supposed to somehow stop the German armies. That was never its purpose. However, had it been longer, it could have prevented Guderian's and Rommel's forces from turning the flank of the French armies. Now, as for the British, as far as I know, the nine divisions of the BEF were all the forces they were willing to commit, and they were perfectly established, at least as well as other allied forces, anyway. Whether the French were "willing" or not to be occupied has no bearing on military operations, I'm afraid, and in any case, it would be more accurate to say that the French were unwilling to lose another generation on top of being occupied.

(it would be more accurate to say that the French were unwilling to lose another generation on top of being occupied.)

This is certainly a key to the attitude of the French. Their experiences rank them right up there with the Jewish in respect to the lesson that adversity begets wisdom and wiliness.

For the Wehrmacht, the Sichelschnitt was the most risky action imaginable. Failure would have meant the encirclement of their entire tank force and immediate defeat. The generals-staff of the OKW was far from a consensus when the maneuver was introduced. From what I read so far, the only reason the Sichelschnitt was attempted was that in early '40 the entire invasion-plans for Fall Gelb fell into allied hands and the Sichelschnitt was the only plan B the Wehrmacht had in their drawers.