Answer:
A. Would be theirs, as long as they stuck to the plan.
Why was the Battle of the Marne significant in history?
It's rather a case of right place, right time. The German flanking plan, known as the Schleiffen Plan, was largely misunderstood by the French in their initial maneuvers, leaving an unlocked rear door.
When it was evident that the axis of progress through Belgium was the major German effort and the German goals were known, Joffre repositioned his forces to counter this assault. Joffre made smart tactical choices as he retired to the Marne's positions. Shortening communication and supply lines while reorganizing dispersed troops are all benefits of a well-planned retreat.
In order to destroy the French army in detail, Moltke must move to fight them while simultaneously expanding his administrative lines. However, he cannot push on Paris while the French army is still in tact just off to the left.
Joffre doesn't now need to annihilate the German army; all he needs to do is keep them out of Paris and the coast of the English Channel. The point is that Joffre can't defeat the Germans in a decisive battle, but if he keeps them there or, better yet, drives them onto territory that will allow for a thorough and German-evicting counterattack, the time he buys will sap his opponent's material strength while he gains more every day from the UK and foreign Colonial forces.