The second reason is that the BEF had, unbeknownst to the Schlieffen Plan, crossed the channel and fought the German first army, under the lead of Alexander von Kluck, at Mons in Belgium which held the German first army up for two days. It may have been longer if the BEF hadn't heard that the French Fifth army was retreating, so the BEF did likewise. Then they marched south 125 miles to the River Marne. If the BEF hadn't retreated, they may have either stopped Kluck entirely or the entire BEF may have fallen.
The Schlieffen Plan had anticipated, and counted on, the Russian armies taking longer to mobilise. However, the Russian Armies invaded Prussia on 17th August. Moltke sent half his right wing to the German Eighth army which left the right wing weakened and more vulnerable. Had the Russians taken longer to invade Prussia then Moltke wouldn't have sent more men to Germany's eighth army and then no other armies in the battle would've noticed a weak spot in the German defence.
Joffre now realised that the Germany was attacking most from the left and dispatched the Army of Alsace, the French Sixth army, to his extreme left that covered and protected Paris. If Joffre hadn't noticed this then he probably wouldn't have dispatched the newest army and Paris' defence would've been weaker.
The fifth reason seems very superficial but it very relevant. As the French government retreated to Bordeaux, the German First and Second armies reached then River Marne where they...