Well, I think a lot depends if France decides to play smart (achieving a decent victory, but not destruction of Germany) or goes possessed by the ghost of Napoleon. In that case France is likely to throw somebody else over herself (*cough*Britain*cough*) and dinamitates the possibility of dividing the Germans.
Absolutely agree. I don't think that France would get Britain to intervene in this war, because of the inherent initial instability of Boulanger's regime. However, now that France has defeated Germany handily, France will probably continue their naval building program (I recall that France spent more on the navy than Germany pre-WWI) and thus be percieved by the British as the main threat in Europe.
In my mind, a good result for France would be return of Alsace-Lorraine plus an enlarged Saarland. As the war is started by the Prussian militarists, a big setback can encourage the Southern German States to break from Germany (only, I repeat, if France plays nice and does not mention of natural borders nor annexation of any inch of these southern states).
No way. Germany has united, and people think about themselves as Germans. A military defeat will not break Germany apart. If some of those southern German states attempted to break away, their would be significant opposition both within those territories and outside those territories (ie the German Army and assorted paramilitaries), and would require French intervention, which won't happen.
This, possibly combined with some type of disturbs in Northern Germany and/or a general success of the Russian offensive from the other side if there is one (not sure how likely is any of these events) can knee the German Government and force it to ask for peace. France can be then even smarter and ask for the restoration of Hannover, making Britain and Austria smile and not willing to discuss France' success. France does not need to ask for the removal of the Kaiser, even; in the aftermath of the defeat his position is so bad and unstable that the own German Empire is likely to collapse on their own and be replaced by another loosely German Confederation.
With this kind of swift French victory, possibly combined with a Russian intervention and definitely a post-war Franco-Russian alliance, the British are not going to want Germany cut up. The Brits will probably now view the Germans as the counterbalance to the rising threat of France and Russia. The Austrians certainly will not want Germany cut up, because by 1889/90 it is clear that Austria is probably no longer really a great power, and it needs German strength to maintain her territorial integrity (against Italian, Slavic, and Russian designs).
Also the Germany Empire was not ready to split up. Basically, the German Empire has something of a monopoly over power that comes out of the end of a gun, and unless a foreign power is ready to directly intervene in German affairs and end that monopoly, the German Empire will stay internally intact.
That, of course, if France plays nice. If Boulanger goes crazy and asks clear that he wants to annex half of Germany, he would just put the Germans together and ready to defend the homeland, and make them the victims in foreign eyes. Divide and Conquer!
If Boulanger made it clear that he wanted to go to Berlin, I think that he would probably find himself suffering an accident, or being arrested. He just took power in a coup, not exactly the most legitimate form of getting executive power, and needs a quick victory so he can focus on shoring up his internal support.