On september 1st, 1914, (after nothing else happening different than historically) Lord Kitchener suffers a flat tire resulting in a crash into a tree.
As a result, he's not around to inform John French to not retreat all the way to (or across) the Channel. While it doesn't cause the BEF to retreat all that way, the plan is kept semi-active, resulting in a leak to the press.
While it isn't published, an Italian diplomat finds out and contacts Rome. At the same time (give or take) news of the size of Germany's victory at Tannenberg breaks. Italian papers on september 3rd publish the 'news' that Britain is evacuating the continent while the Russians are on the run.
The Italians, ever uncertain of gains if they stay out, offer to enter the war in exchange for gains against France (just a matter of ripping through an empty underbelly). Germany and Austria do not object, and Austria offers a few miles of border correction in the Trentino if Italy declares war on September 5th-6th.
Italy does declare war on the 6th, though the actual offensive into southern France doesn't really start until 2 weeks later.
As a result of the declaration of war, Joffre has to commit reserves south, turning the Marne into a bloody stalemate. Exact events need some work here, but I assume the 6th army is simply reinforced less, so the German 2nd army can beat them back while holding against the French 5th army. As a result Moltke/OHL instead keep up the attack against Verdun and the French armies there, making the battle of the Marne look like a pause in German advances on a small stretch of front (to both sides) rather than a Paris-saving move.
The result is a beginning of panic in French government. Again, exact events need work, but it results in the French position in Verdun collapsing to shorten the front and allow more reinforcements for Paris and the rapidly developing Italian front (unknown to the French, the Italian offensive is about to be bloodily aborted). On September 10th, Verdun is cut off from French forces entirely, and on the 11th it surrenders.
Seeing the writing on the wall, and after much cajoling by the Germans, the Turks begin mobilizing on September 15th after news of a renewed offensive by the German armies in France (actually localized efforts by the German 1st-3rd army to straighten out the Verdun-Ourcq-Aisne frontline, giving a frontline of roughly Metz-Bar-le-Duc-Marne-Ourcq)
On September 17th, the rested French launch an all-out assault on the Marne-line. German 1st army nearly cracks under the strain and has to regroup north of the Ourcq, threatening the whole German position - except the 7th army has arrived just in time to drive west, south of the 1st army, allowing the 2nd and 3rd to hold on the Marne. The French offensive is aborted as the 6th army is nearly cut off from the BEF to its southeast by this new German assault.
A new wave of panic sets in and Joffre orders yet more troops west from the Alsatian front. This fatally weakens the Toul-Bar-le-Duc area of the French front, allowing the German IVth and Vth army to strike out and seize Neufchateau on September 25th, cutting Toul into a salient and threatening to cut off the French 2nd army entirely. Fearing a 'new Sedan' the French armies on the Alsatian front begin a rapid retreat southeast to Belfort, widening the gap for the German IVth-Vth-VIth army to run roughly from Belfort to Saint-Bizier.
The French high command sees no reserves to plug this hole, so the French 3rd and 4th army begin an unwanted retreat southwest (3rd already having lost strength for further Parisian reinforcements) rather than acting to pin the German 3rd army in place. This does much to mitigate the good mood as the Italian offensive is firmly thrown back by September 25th.
On September 22nd, the German 1st army (having recovered between the Ourcq and Aisne) strikes firmly west, crossing the Oise at Compiegne. German 7th races to catch up to protect 1st army's flank as it manages to maintain a steady westward pace until being halted at the battle of Beauvais by September 29th.
On September 30th, the Ottomans declare war on Russia and Serbia.
On October 1st, the German 7th army, reinforced by troops from Antwerp, launches an attack between the Oise and Ourcq (with one corps west of the Oise). The French position to the west now appears close to unravelling as the French 6th army, which stopped the Germans at Beauvais, is now forced to retreat/attack southeast to hold the German 7th, while the French 2nd had only just moved past them for an attack northeast past Amiens.
Seeing a gap forming in French lines both east and west of Paris, the French government (or part of it anyway) secretly offers Germany a free hand against Russia and Serbia in exchange for a status-quo-ante peace. When news leaks the government falls, but the damage is already done as British and Russian negotiators hastily propose a general peace conference given the situation on the ground. Germany accepts in exchange for a lifting of the blockade and the demilitarization and occupation (by Germany) of Antwerp, Belfort, Toul, and Epinal (all still holding, though Toul is effectively encircled and Antwerp is), as well as stopping the influx of British troops into France, and an Italian occupation of Chamonix, Annecy, Nice and environs (mostly, just like the German occupations, to allow an easier progress if the war resumes).
Also some Russian fortifications are taken, but no idea which, and A-H is evacuated by the Russian armies; also, Austrian prisoners are returned to them (Austria was rightly adamant; those prisoners are the best army they have).
The final settlement sees the first institution of a demilitarized zone, on the Lorraine-Lotharingen border (under surveillance by the Germans, so take demilitarized with a grain of salt - and its all on the French side of the border). Some few miles of Belgium and all of Luxemburg join the German Empire. Serbia is reduced to a vassal, and Congress Poland is released under a German monarch. The Ottomans reclaim a few chunks as well, and Italy receives Nice. Germany also gets some French colonies, as after all France lost the war - connecting German East Africa through the French, and giving the Congo to Germany, creating one German blob (little connected as it is).
Everyone prepares for round 2, although noone's quite sure if they should; the Tsar did well enough, so feels the French let him down, while the French feel they had to do all the hard work (and couldn't beat Germany alone). Also Austria-Hungary comes out looking very shaky, especially as Serbia defies the treaty for the next 6 months (openly) or 3 years (before peace really is established under the new Austrian puppet). Italy's bitter over not getting Tunisia and Savoie. And Britain is thinking intervening in Europe was a damned fool thing, but at least Germany didn't run away with all of Europe.