The Franco-German border was heavily fortified prior to World War I; that's why Germany went to so much trouble to bypass the area in the first place. The French tried offensives into Alsace-Lorraine in the early part of the war in OTL and was soundly defeated; I'd assume that without the planned attack through Belgium to relieve French pressure on the A-L front and take up the bulk of German manpower the A-L forts will be even more strongly held than OTL so the outcome is not likely to change.
Also, with no German attack on Belgium British aid on the Western Front will probably at least be delayed and/or weakened compared to OTL, particularly if Germany is taking a defensive posture vs. France. IMO, when Britain enters the war they would be much more inclined to use their army in a Gallipoli-like independent campaign than to commit it to the Western Front under this scenario.
Removing the attack on Belgium will also make it much easier for Germany to get supplies of nitrates from abroad, as they will not have alienated a large number of previously neutral powers. This is doubly so if British entry into the war is delayed, thus giving Germany much easier access to the world market due to no blockade.
If the bulk of German manpower is focused on Russia the Russia pursuing the same strategy as OTL would be very unwise; the German offensive could quite likely end up cutting off the Russian forces moving against Austria-Hungary and gaining a victory even greater than they managed at Tannenberg. The salient in the Russo-German border formed by Poland is just begging for a major offensive to create a huge encirclement of Russian forces, something of which the Russian general staff is well aware. IIRC Russian plans in the event of facing a joint offensive from the German and Austro-Hungarian armies were to pull back from the Poland in order to have a shorter and more defensible frontline.
Also, logistics probably will not be as much of a problem in World War I as they were for the Nazis; the nature of the war makes rapid advances unlikely and requires solid railroad supply lines to be established to support any offensives. Furthermore, the WWI Germans would not ignore logistics as Hitler was wont to do, nor would there be as much deliberate antagonisation of the local populace.
World War I ≠ World War II
If Britain tries to fight on from French territory then Germany will demand that the French government remove them or be considered in violation of the cease fire. If the British refuse to leave then France will be forced to either resume the war with Germany or declare the British an invading army and respond appropriately (i.e. to expel the British by force).
Further, the odds of any "Free French" showing up are extremely low; the Third Republic would still be in place rather than the much less legitimate Vichy regime established in World War II, and years of trench warfare would leave the French soldiers in the field much more exhausted of war and inclined to go home and rebuild than six weeks of blitzkrieg.
I won't even mention the assumption that the US would still enter the war in 1917 despite a completely different progression of the war when compared to OTL. There's no "Rape of Belgium" to turn opinion in the US against Germany as occured in OTL, and without most of the neutrals already alienated Germany will be much less inclined to launch Unrestricted Submarine Warfare when Britain enters the war. IMO, the US is likely to stay neutral for the course of the war and make a ridiculous amount of money selling whatever it can to both sides.