Oooh, this is one of my favorite topics!!! So the answer that is most commonly accepted is syphilis. So I'll refer you to a previous post that I wrote on this subject on r/Medicine for a lot more information about the dramatic appearance of syphilis in Naples in 1495 (along with a really cool woodcutting by Durer of what was likely one of the first syphilis patients in the West).

Let me start my quoting that previous post with some background (though with embarrassment I'll give the caveat that I'm not an historian, but a physician/podcaster and this was written not with the political situation in mind, but the medical):

Syphilis is caused by a corkscrew-shaped bacterium called Treponema pallidum. It is easily transmitted through mucosal contact, and most infection is therefore sexual in nature (though mother-to-child, both via blood, and during the birthing process, were common). We now divide the disease into three stages -- during primary syphilis, a painless ulcer called a chancre forms at the site of inoculation, naturally usually on the genitals. Months later, the patient develops flu-like symptoms, a rash (classically on the hands and feet), hair loss, and meningitis. This is secondary syphilis. In its final stage, the disease causes granulomas to form all over the body (gummas), which can interrupt organ function and disfigure the patient. The vasculature is affected (especially aortitis). And of course, neurological manifestations appear -- tabes dorsalis, the degeneration of the dorsal columns of the spinal cord; dementia; and the dreaded general paralysis of the insane (GPI).

As far as infectious diseases, syphilis is fairly unique because we can date its appearance to Western doctors to a single year -- 1495 -- when a great, mysterious plague hit the city of Naples. This first manifestation of syphilis was far more violent than the disease we know today. Patients would have diffuse ulcerations and gummas in a matter of weeks, as the man in this image. They would show signs of what we now recognize as sepsis. And the mortality appeared to be much higher.

The reason why this first manifestation of syphilis was so deadly likely relates to its origin. In 1494, Naples was taken by a French force of 25,000 mercenaries from across Europe, some of them Spaniards who had just returned with Columbus from the New World. In 1495, the neighboring Italian cities banded together to evict the French, and then were welcomed by horrifying tableaus like this man. The mercenaries disbanded, taking the disease with them back across Europe.

But I actually want to talk a little bit more about the controversies surrounding the origin of syphilis, and how advancing medical, anthropological, and genetic evidence has slowly shifted our understanding of the origin, and how there are still some controversies today.

By the first years of the fifteenth, European doctors had largely accurately described the first and second stages of syphilis -- and a consensus was emerging on where it came from. A physician who had treated Columbus' men reported in 1520 that he had seen similar findings (esp. the painless ulcer; chancre) prior to returning to Hispaniola. And Spanish doctors realized that the disease was endemic on Hispaniola. The medical community was slowly coming around to what is now called the "Columbian Hypothesis;" that is, as your question asserts, the disease was the smallpox antithesis, transmitted from the North American natives back to European colonizers. By the nineteenth century, the Columbian Hypothesis was fully accepted, even though many of the details had yet to be worked out (most notably, gonorrhea was thought until surprisingly recently to be another form of syphilis).

Then in the late nineteenth century into the early 20th century, anthropologists began to study bones in depth. They found many bony findings in pre-contact Europe that appeared to show the effects of syphilis (esp destruction of the cortex of the bone, and ulcerative lesions). There were also studies on Egyptian mummies that purported to show lesions due to syphilis. Finally, the new field of paleopathology looked back to Greek and Roman medical writings, and found cases that they felt could describe syphilis. Slowly, a new consensus was growing -- essentially that syphilis was an ancient disease that had existed in both the New World and the Old. The idea here was that the outbreak in Naples had been an especially virulent mutation of endemic syphilis, which had "burnt" itself out -- this actually makes sense given the decreased virulence of other infectious diseases, especially tuberculosis, as there are selective pressures to decrease mortality for the organism.

Finally, in 1905, T. pallidum was seen under darkfield microscopy, and doctors realized that the far less severe diseases of bejel and yaws were also caused by T. pallidum; both of these are present in the old world. A "hybrid hypothesis" was developed that stated that T. pallidum caused disease everywhere, but that local factors could cause it to present as syphilis versus bejel or yaws. These "local factors" changed in the 15th and 16th century, leading to the syphilis outbreaks.

So if we were having this conversation fifty years ago, the pre-Columbian hypothesis was dominant, and in fact you'll find plenty of references (including the pathology text book I used in medical school!!) stating the pre-Columbian hypothesis.

So how has the Columbian hypothesis come to be accepted again? Well, first of all, DNA analysis quickly did the hybrid hypothesis away; we can see that though syphilis/bejel/yaws are all caused by the same organism, there are evolutionary divergent.

The best evidence against the pre-Columbian hypothesis comes from paleopathology and anthropology, not DNA analysis. I'll put the link to the review at the bottom, because it's fascinating. But essentially, researchers developed as "osteotype" -- that is, bony findings that are caused by syphilis but NOT other diseases (if you're curious, the osteotype was composed of bony gummas and saber shins -- because ONLY syphilis will cause those findings). What they found is that the syphilis osteotype was not found in a single bone pre-Contact; the findings before 1495 were "sensitive" but not specific; that is, they were found in syphilis, yes, but also in other diseases. In the Americas, however, the osteotype was commonly found prior to 1492, and in fact the migration of syphilis across the continents could actually be tracked.

The Columbian hypothesis again reigns supreme.

So to get back to your question -- the initial Neapolitan syphilis outbreak certainly APPEARS to be because Europeans lacked natural immunity -- though could also be because the serovar brought back from Hispaniola was especially virulent, and selective pressures made syphilis less deadly over time.

I hope that helps!

EDIT: Forgot the include the reference I promised.

• Rothschild, BM, “History of Syphilis Clinical Infectious Diseases.” 2005; 40:1454–63

There's always room for discussion but perhaps the section Impact of indigenous diseases on the Europeans from our FAQ will answer your inquiry.