It ultimately depends on how the British and French react to the loss of Amiens; do they immediately counter attack and get back the city, or do they panic and pull back in fear of a German advance on their supply centers? If they pull back then German forces can consolidate, knowing that they can't advance further and have just cut a major artery that will back attacked as some point; they of course will have to deal with building up the infrastructure to hold it, which they had lots of trouble with IOTL.
If the Allies focus their attention to the south, which IMHO they would, either for preparing a counter attack within a matter of weeks, then the Germans can launch Georgette with a better chance of success than IOTL. If they can get that moving before the Allies counter attack Amiens or launch it simultaneously, which is doable IMHO, then the Germans can breakthrough there. I don't know how the Allies would react at that point; it would make sense for them to follow through at Amiens, but I think the British would panic and pull out of the Amiens counter offensive to reinforce Flanders.
I assume that Amiens falls if the Allies opt for a quick counter attack, but they might not for a variety of reasons, especially if Hazebrouck falls.
If the Allies lose both cities and fail to recapture either, then they are in for a very serious political mess, as British forces have to pull back to the Channel port areas and pull out much of their forces north of the Somme. This will cause a very serious crisis in France, especially if the Germans follow up with further attacks toward Paris.
But we are in a very tricky situation politically; Clemenceau has already thrown Caillaux in jail and charged him with treason, effectively eliminating him from politics, so unless there is a major movement to get him cleared and reinstated in the French government, he is not a factor.
https://en.wikipedia.org/wiki/Joseph_Caillaux
I'm not sure if Clemenceau could be replaced at this point barring revolution or assassination, as he had found a way to make himself virtual dictator of France for the duration of the war. Revolution is not out of the question though, which might spell the end of France; the question is whether the French army holds together with Germany virtually eliminating the British from the fighting for most of the rest of the year; it also doesn't help that Germany has just captured enough supplies to carry their army through winter if need be.
If the French buckle under a Chemin-des-Dames offensive like IOTL, then there is the possibility we could see the French army start to disintegrate, especially if more riots break out in favor of peace in French cities, which had started in late 1917-early 1918 and was IOTL put down by the French cavalry. There are just to many variables to say for sure, but morale of the French is going to be the primary factor in determining if the war goes into 1919.