Well, as I see it, the best way is a distraction. THe only possible distraction would be Britain. If the Great Game between Russia and Britain becomes more hostile and active, Russia will reduce its focus on the Balkan, thus reducing tensions with A-H and A-H-friendly Germany. Meanwhile, a Britain willing to be more hostile to Russia may be willing to be hostile to France, too. In such an environment, Russia and France might of course shack up together and incidentally be seen as a threat to Germany - but Russia might also seek a German alliance (given Germany's growing strength at sea) while not wanting to be distracted by France's squabbles with Britain (instead preferring France to distract Britain from the German-Russian alliance).So, Russo-German breakdown equates to a French-Russian rapprochement and encirclement, but the reverse does not hold? As in, it doesn't necessarily mean France would kiss up to Germany if the Germans have Europe's Gendarmes as their allies - since then the Germans would have no need for the French advances, and it would also imply a France - Germany - Russia axis which historically has never really happened.
In order for the French and Germans to become friends or even allies, the equations of power configurations you outline implies that Russia must in some way become hostile to Russia, and be closed off as an alliance option for France, for France and Germany to draw closer? Can anyone think of how that array might come about?
Of course that does lend itself to a grand alliance of the continent as was nearly seen during the American Revolutionary War - and it will end as soon as Britain has been forced to be less actively hostile and instead goes back to a slightly-lower-than-historical level of tension-seeking and a slightly higher level of tension-avoidance. There might be one more or less punitive peace, losing Ireland or some chunks of Africa. Of course this would be far worse than historical for Britain, so this does require Britain to be given the idiot ball for at least 1 or 2 crises.