Why an Italian Savoy front would not guarantee Paris

Would Italy joining the Central Powers in 1914 make the fall of Paris inevitable through Savoy?

No; the Alpine front, poor Austro-Italian cooperation, and additional Allied imperial troops make a quick route to Paris unlikely.

Italian entry for the Central Powers would not automatically bring down Paris. Italy and Austria-Hungary had recently fought over Italian unification, so their armies would not instantly operate as a seamless coalition. The Savoy frontier contains mountains and fortifications, while Paris lies far beyond them and the northern front was already stabilising. Britain and France could call more Indian formations into Europe and accelerate plans for African formations to fill gaps. Such mobilisation would be costly and slow, but it gives the Allies options beyond stripping the existing French line. The counterfactual creates a dangerous additional front without turning geography and coalition politics into an effortless breakthrough.