Your best PoD is probably the Battle of Mons.
Had Kluck continued on his original path (rather than moving closer to Bulow as Moltke ordered him to) he would have crossed the Franco-Belgian border(and the Mons-Conde Canal) further west than OTL, opposed by only a few French Territorials. He would thus have taken the BEF in flank rather than head-on, and it would not have had the canal as a defensive position. After that things get much more iffy, but had the BBEF been pushed back eastward rather than south, it would have been clogging the roads directly behind the French V Army, and right across Lanrezac's line of retreat. So the Germans have at least the chance of a "Tannenberg West" with both BEF and V Army destroyed.
This is very bad news for France, but not *necessarily* fatal . By Sep 5 there was a big bulge in the front line, so if the French straighten it by pulling back from Verdun to a more or less straight line from Toul -Nancy to just north of Paris, this may enable them to release enough troops to cover the remaining gap between Paris and the Channel, which the front may hit somewhere near the mouth of the Somme. So you still get trench warfare, but along a line quite a bit further west, so France loses more of its industry, and Paris is going to have an awful time, perhaps ending up a bit like Ypres did OTL. But in this situation France still hasn't collapsed, at least not right away.
Possible butterfly. This western "Tannenberg" would go some way to overshadow the actual one, so maybe Hindenburg (and so Ludendorff) doesn't achieve the same prominence as OTL.