IMHO Zola summarized the feelings of a large number of elements in France with his letter. Letter or no letter it was the actual events of the affair that prompted Herzl's "Die Judenstaat". Similarly Germans did not slack off on their espionage because of the Zola piece, if anything if the French continue to focus on Dreyfus and never get to Esterhazy then the Germans have an asset still in place. Once the facts of the affair and the espionage came to light it took some time for the French Army to heal, if this takes place closer to WWI it could be worse for France, maybe not as the German failure of the Schlieffen Plan was due more to internal failings of the plan rather than brilliant performance of the French Army.
You are also adding a POD of Dreyfus dying, OTL he was reinstated in the army and died of natural causes prior to WWI. If Dreyfus is executed, and then later (as OTL) shown to be a fall guy, then the consequences for the French military will be worse - an innocent railroaded to Devil's Island is bad, one decapitated by the guillotine much worse. I have no evidence for this, but I suspect that the powers that be in the army knew the case was shaky and that is why his sentence was not death, which would have been perfectly legal for this crime.