The question is how does Paris fall? One possibility is that Von Bulow keeps up with Von Kluck's first army, taking away the gap that the British were able to exploit in the battle of the Marne. You could also find a way to keep Belgian resistance around Liege a bit less troublesome to defeat. Perhaps some more success killing or capturing French troops before the Marne is also a possibility.
The Marne is the best bet for an early French defeat. The war hadn't bogged down into an endless siege and was still a mobile campaign. I don't see how Paris could withstand a siege after the Marne as the French garrison had all been sent to the front during the battle. (That must have been one large taxi fare). The Race To The Sea in this circumstance would be between the British trying to reach the channel ports and the Germans trying to cut them off.
Without the huge loss of life on the Western Front Europe today would be a very different place. In a sense we are all survivors of that war as our Great Grandfathers were the ones who made it back. Thanks to ideas like the Pals Battalians whole communities in Britain lost a generation in as little as a few days on the Somme. Post war it became impossible for many young women to find husbands due to the losses, and because of the Children who were never born Britain face severe manpower shortages during and after WWII which led to the mass imegration of the 50s and 60s. Something that was repeated in France and to a lesser extent West Germany.
In my opinion the Twentieth Century can be best described as The Great War and its aftershocks.