The notion that Falkenhayn wanted to "bleed France white" comes from his own memoirs, published after the war in 1922. There's no documentary evidence that his intention was really that at the time when he planned the Verdun offensive in the winter of 1915-16. And given Falkenhayn's penchant for secretism, we will probably never know.
What the German commanders in France made abundantly clear is that if such was Falkenhayn's intention, he never told any of them so, not even to Schmidt von Knobelsdorff, the Head of Staff of V Army who was the real enforcer of Falkenhayn's will on the battlefield (especially after time went by and Falkenhayn's relationship with Kronprinz Wilhelm deteriorated). That caused a great deal of frustration amongst them, because they never understood what was the real objective of the battle (according to Falkenhayn). To them, it was to conquer the fortresses of Verdun. And the way the German attack was managed and organized was not very conductive to that goal from the very start.
If the objective was indeed to occupy the fortresses, the Germans wasted miserably the initial attack, when a decided push against a devastated French defense would have been an almost sure success. But their cautious approach allowed the French time to reinforce Verdun and turn the battle into a meatgrinder for both sides.
On the other side, for the kind of battle that Falkenhayn apparently wanted Verdun was a good choice. It was near major rail lines controlled by the Germans, and thus supply (especially artillery shells) and reinforcement was not a problem, while on the contrary Verdun had very poor rail connections on the French side. And the numerous hills on the east side of the Meuse also allowed for excellent artillery positions from which the German long range guns could shell Verdun from relatively safe and hidden placements. But if the battle was to be a long one, not attacking from the start also on the west bank of the Meuse (like the generals of V Army had wanted) was a bloody mistake, for it allowed the French artillery three months to slaughter with impunity the right flank of the German Fifth Army that was attacking the French positions on the right bank of the river. And when they finally managed to mount that attack and silence the French guns, it was at a very high cost.
Falkenhayn also was a bit naïve to think that the French army of 1916 would be the same army it'd been in 1914, when the Germans had enjoyed an absolute superiority in heavy artillery. By early 1916 the French had closed the gap, and at the Verdun battlefield they managed to deploy an artillery display that matched the German one. When general Von Gallwitz first arrived in the battlefield in March 1916 half of his staff, who were driving in a car in front of him, were blown up to pieces by a French 105mm shell. This showed him that the French army would be a very different enemy than the Russian one.
