Sep 1 is too late. The crucial point is not the Marne but the Frontiers.
If whoever replaces Moltke allows Kluck to move further west, then by the time of Mons he is well placed to take the BEF in flank, and drive it back across V Armee's line of retreat. If both are destroyed, there may never be a Battle of the Marne as we know it, as the remaining French armies would have the unenviable choice of staying were they are and risking encirclement, or else abandoning the fortified positions along France's eastern border and falling back westward, which allows the opposing German armies to pursue and exposes them to a double envelopment. Not good either way.
By the time of the FBotM, the best Germany can do is hold more ground than OTL and get a Western Front much deeper inside France, but still not including Paris. This change could lead to a CP victory in the long term, but not an instant one.