The answers that have been provided so far are correct in one sense, but they skip over the key to your question. The key to why a reaction is catalyzed by a substance has to do with the mechanism, in particular the rate determining step. The answers above do not show that step or discuss it, but rather they show a step which precedes it, namely the protonation of the bridge oxygen. It is true that this step is important, and that it involves the hydrogen ion. But it is the following C-O bond cleavage step that is more likely the rate determining step.
For a detailed answer to your question see this post which references a publication that solved the mechanism details:
Hydrolysis of Sucrose over Sn1Ac or Sn2Ac
Based on that reference, I do not believe @Tyberius is correct in saying, “Water then binds to the fructose ring, breaking its bond with the acetal linking O”. Rather, water only comes in after the oxocarbonium ion has been formed in the C-O bond cleavage step. The detailed answer to your question is that the presence of an acid makes that C-O bond cleavage step happen quicker.