Enveloping Paris from the west as well was indeed a part of the original Schlieffen plan, but that plan hadn’t been quite as successful as the Germans had hoped it would be. Which was not too surprising, because they had committed fewer troops than originally intended by Von Schlieffen, and the reason for that was, that they also needed to fight Russia.
As a result, when the Battle of the Marne started, the front line ran north-south from Ypres in Belgium to a point some 50 to 60 miles north of Paris, and from there, mostly east-to-southeast towards the Franco-German border. Sending an army westward and then south to arrive west of Paris, would have been a high risk operation, exposing that army to counterattacks on both flanks. In the original Schlieffen plan, a much larger area to the north would have been overrun, and the encirclement of Paris would have involved forces arriving from that direction.
So while I agree that the German High Command probably planned and hoped to win the war that way when it started, I’m not sure that encircling Paris from the west was still their intent in early September. Accounts of the situation and events and especially of the various plans are not always consistent, and I may have misinterpreted some of them, but it seems that the German idea was to break the French lines east of Paris, and thus separate the French armies in the east of the country from the capital, which would then be captured. The actual encirclement would only have been partial.
Why exactly that plan went wrong, can probably be attributed to various courses. The Germans may have underestimated the strength of the Paris garrison, or may have been misinformed of the whereabouts or even the existence of the French Sixth Army, that had just been formed. This account by Von Kluck, the commander of the first German Army, casts blame on Von Bulow’s Second Army for not protecting the right flank of the advance, and it’s illustrative of the overall difficulty in coordination and communications. Of course, it was written by a man who had to defend himself for the failure of the entire operation. Another factor may have been that troops had recently been transferred to the eastern front, because the Russian threat seemed bigger than it turned out to be - the Germans didn’t know beforehand that they would be as successful as they were at Tannenberg.