Goldfinger: The plan that von Manstein came up with in 1940 was only superficially the same as the Schlieffen plan.
Schlieffen wanted to bag up the French army by outflanking them on the right, and forcing them to surrender quickly, so the Germany army could then go East to fight off the Russians.(Its a hell of a lot more detailed, but that's the basic idea)
This did not go to according to plan
Manstein's plan was a bit more clever. Knowing that a frontal assault on the Maginot Line was militarily stupid, the French and the British expected a replay of the Schlieffen plan... a strong right wing wheeling into Belgium and possibly Holland. As a result, they were ready to march north into Belgium the moment the Germans attacked (Due to the Belgian King being a bit prickly, he refused to allow them in beforehand, and then screamed for help when they did). Guessing that that would be the Allied response, von Manstein proposed that the center-right of the German line be the strongest, to cut off the advancing Allied armies moving into the Low Countries on their left. This was discounted due to the heavily forested terrain in the Ardennes.
This worked quite well, with results we all should know about.
However, having said all that, the Schlieffen plan almost worked. The critical battle isn't what everyone talks about "The Battle of the Marne", which wasn't a single battle, but many engagements, most of which were nowhere near the river Marne.
The crucial one in my opinion was the battle on the right side of the battle, south of Verdun at Fort Troyon. There, the (I belive, I'm going off of memory here) Fifth and Sixth German armies attempted to pinch off the fortified position of Verdun in 1914(Its not mentioned much at the time due to wartime censorship... Verdun being a rather important symbol of France, and then overshadowed afterward by the Battle of Verdun in 1916.
The French soldiers refused to give up, and defended the fort and the Verdun position was not cut off (obviously). If the Germans had, they would have been able to spread their manpower more evenly and been able to at the very least secured a more defensible position that many miles south of where they had to... with Verdun in French hands, the entire German army was at the end of a tenuous supply chain, with an untenable defensive position. The OHL made the logical choice to retreat to save the army, and regroup for another round.