Von Kluck reports that incident as well, but in a slightly different tone: French cavalry had attacked the airfield near La Ferté Millon. When the motor column of 1st Army's staff approached that spot, they were warned about the incident. They stopped and formed a defensive position - but did not encounter the enemy. As it then turned out, the enemy cavalry had already been dispersed by other German units. Less drama thus, nevertheless Kluck thought 'that the valiant enemy cavalry had missed a great opportunity.'
Suppose, they didn't miss the great opportunity: The most senior corps commander, in this case von Linsingen, II. AK, would have taken over. There might not even have been a break in the battle, as the incident happened in late evening and all orders for the following day had already been issued. The demise of an experienced army staff (operations section) would, however, have become palpable in the days to come, especially in the retreat to the Aisne and the formation of the defensive line there.
http://www.firstworldwar.com/maps/graphics/maps_12_marne1914_6.jpg
The problem is that the Staff of the First Army received the order to retreat on September 9 at noon while the Second Army was already retreating since the morning. Which means there are a lot of chances that the First Army will go on with its attack against the French Sixth Army for at least a few hours (before Hensch manages to reach Lisingen and to inform). It could be enough for the BEF to reach the Ourcq from the Marne (less than 15 kilometres between the two): in which case the entire BEF would be just behind the II and IV Korps which are already worn out and currently attacking the French Sixth Army southern positions. Basically these two corps are doomed if this happens and the First Army will lose 90 000 more men within 24 hours.
In which case, by the 10th, the First Army is reduced to 6 Infantry Divisions against 11 French and 5 British Divisions and forced to fight in a salient with a dense forest in the north, the French Army in the West, the Ourcq river in the East and the BEF in the South East. The only way for the First Army to retreat is to retreat eastwards, between the forest of Villers Coterets and May en Multien (a village on the Ourcq river): this passage is barely 8 kilometres wide, with small bridges you have to cross while the BEF is advancing northwards from May en Multien towards the Forest of Villers Coterets. At the same time, the German IX Corps is NORTH of the forest and thus separated from the bulk of the First Army. So the First Army is basically trapped in a mini-Falaise pocket and will only be able to get a portion of its troops out of this gigantic ambush.
My guess, the IX Corps, still relatively frest, would be able to retreat by following the railroad north of the forest but the other Corps will be lucky if they can savalge 40 000 men while abandoning all their heavy equipment. So the First Army with luck is reduced to 80 000 men and separated into two formations while the VII R. Korps hurries the frack up to reach the Aisne after Maubeuge and while the Seventh Army must hurry the frack up as well since this Army must now fulfill its role AND the role of the First Army at the same time for the coming battle of the Aisne.
https://upload.wikimedia.org/wikipe...king_moves,_15_September_-_8_October_1914.jpg
Joffre will be even more convinced than OTL that he has to bypass the Chemin des Dames from the West (between Compiegne and Noyon), while the Seventh Army, with at best 12 Divisions (6 Divisions properly belonging to the Seventh Army, at best two exhausted Corps from the former First Army and lacking heavy equipment, notably heavy artillery, plus the VII R. Korps coming from Maubeuge and thus relatively exhausted), must hold the line against at least 15 French (Sixth Army plus Territorial Divisions of General d'Amade near Amiens and able to use the railway system to quickly reach the front) and 5 British Divisions. Plus Joffre can use the railway system as OTL to quickly send Divisions from the East to the West while the Germans have to do it mostly on foot.
Finally the German Seventh Army must defend a elongated frontline between Noyon and Craonne while OTL it just had to hold the line against the BEF from Soissons to Craonne. The frontline just doubled but the troops allocated for this task are 50% lower than OTL. Basically, the battle of the Aisne is way shorter and the French Sixth Army is very likely to take Noyon before the heavy rains of September 19, thus bypassing the Chemin des Dames and threatening Heeringen's right flank. So the the Seventh Army is again forced to retreat before Rupprecht and his Sixth Army arrives to stabilize the situation.
After the Chemin des Dames, the best defensive positions are along the Ailette rivers, with ridges just South of Laon. Problem, this ridge isn't as elongated as the Chemin des Dames (it stops after east of Chauny) after this ridge, the terrain is FLAT until the Ardennes and Charleville-Mézieres. So in order to cease their retreat, the Germans must hold the Laon ridge at all cost (job for the Seventh Army) while Chauny and the territories north of this city must be protected in order to secure the ridge's right flank (job for the Sixth Army). My guess, Heeringen and Rupprecht being competent generals (plus Falkenhayn not being incompetent either), would be able to hold the line, at least partially (the exhaustion of the French Army would help as well). The Germans would be able to hold the line along the Oise then Sambre Rivers while still holding Maubeuge which would be turned into a formidable fortified aera. Then the German would at least able to hold Belgian lands east of the Dendre river (perhaps even holding the line along the Scheld river but that's less certain while still possible). Antwerp would still fall and Germany would still have the salpetre.
But France keeps his coal (plus a little Belgian coal) while the Race of the Sea is a decisive Entente success. Germany tooks a further 100 000-150 000 or so permanent casualties (killed or captured) compared to OTL but keeps most of industrial Belgium (but loses most of agricultural Belgium which is controlled by the Entente) and still firmly controls the Luxembourg and French iron mines (even if OTL they didn't use the French mines THAT much). Globally a win for the Entente.
Possible Frontline in October 1914. The Germans could perhaps be more successful and hold a Scheld river line though.
PS: BTW Belgian fate would be interesting: Free Belgium would a Flemish one with most of the soldiers and population speaking flemish plus Free Belgium would have the agriculture to feed them (see the rich plains of Flanders). On one hand it probably reduces flemish collaboration with Germany to zero. OTOH, Flemish people would have the legitimacy to ask for linguistic/cultural and perhaps political concessions to Albert I. I dunno here, would a expert on the subject and I'm not.