In Crimes of Grindelwald, set in the 1927, it is stated that there has been "a hundred years of peace" between Muggles and wizards. This means that in the 1820s there was some magical conflict going on which related in some way to the Muggle world.

This makes sense, as wizarding conflict and Muggle conflict tend to coincide - Grindelwald's global movement and the Second World War, Voldemort's domestic campaign and the Troubles. It's not that there are causal relationships between the conflicts, but rather that the spirit of the times, which bridges both magical and Muggle worlds, is one of conflict. So during the period of the Napoleonic wars, one would expect to find the wizarding world in conflict also.

So what wizarding conflict involving Muggles can we imagine that is distinct from Grindelwald and Voldemort's positions?

• In Grindelwald we have the idea that the statute should be discarded and wizards rule over Muggles.
• In Voldemort we have the idea that the statute should be strengthened such that wizards and Muggles are completely separated to maintain the purity of the magical world.

 

Depending on who initially signed the Statute, this could (vaguely, I'm not exactly a history buff) be an era where the initial signatories attempted to force the statute on others, which would tie in to the imperial expansion efforts of European powers at the time. However, this is just a repeat of "we want the statute to be stronger/weaker".

Alternatively (although remaining within Europe), the HRE was dissolved in 1806, and fifteen-twenty years gives you some further wiggle room. I'm sure someone with actual historical knowledge could point out a few houses that rose to greater prominence during that time, and you could have them be re-awakened squib lines, or have muggleborns appear, or have had wizards/witches marry into the family. At which point the question arises for wizards - can a wizard hold a muggle title? Should the muggleborns be taught, changeling'd, killed in their beds, or left to discover magic themselves?

You can have that develop into a three way war:
One believes that wizards should never hold muggle titles, to distance the two worlds. One believes that all muggle titles should be held by wizards, to keep the muggles in check. And the third believes that bloodlines are the important part - it doesn't matter if the title is held by a wizard or muggle, but the family should retain their titles.

 

It's easy to imagine that the nature of the conflict lies in struggles for power, but I'd like to suggest a different idea: The Industrial Revolution took place until around the early 19th century. While muggles were hardly able to create anything of interest for wizards before, suddenly, they started inventing machines that could be of use to even the magical population. Of course, wizards are able to greatly improve muggle machines with magic, but still: The current magical world includes many objects of obviously muggle origin (the radio, cameras, daily newspapers etc). Many of these were invented later, but the Hogwarts Express- perhaps the most famous piece of muggle technology- was introduced in 1830 (that's what the Wiki says).

It seems likely that changes like this would not be accepted by all parts of the population. While conservative purebloods would surely protest, others might see the rapid progress of Muggle technologies and sciences as an opportunity to combine both worlds for even greater achievements. This resulting in a violent conflict seems quite plausible.

 

It depends on the structure of goverment prior that time. If the wizarding world mirrored the muggle one in that political power was hereditary, or concentrated within a few people (perhaps in the Winzengamot, given the absence of aristocracy/kings), you could have the revolutionary spirit of the times bleed over from muggles to wizards. Then the conflict would be between those who believed in some form of representational goverment (the modern Ministry perhaps) and the old families in charge, with the conflict spilling into the greater world. Particularly because, you know, conservative wizards would totally blame the muggles for the revolutionary ideas that led to the conflict in the first place, and they sort of would be right. That way you could avoid reashing the same muggleborn vs pureblood conflict. Also , Napoleon was a wizard all this time.

 

The French Revolutionary and Napoleonic Wars, as well as the earlier American Revolutionary War, marked an unprecedented turning point in history. The Ancien Régime began to crumble as the Third Estate ascended violently. The seeds for all of this were sown centuries before, of course, which actually ties in well with the period leading up to and culminating in the International Statute of Secrecy.

In terms of accommodating Harry Potter lore, I could see all of this as a natural result of Muggles being weaned off the occult influences of witchcraft and wizardry and being left to their own devices. The power of the old elites who had always been supported/manipulated by magical practitioners would begin a gradual decline. Materialism would now assume a central role for Muggles, leading to the Industrial Revolution and democratisation of Western civilisation.

Would a Dark Lord of the time have viewed the Statute of Secrecy and its fallout in the Muggle world positively or negatively? And if Muggles had been so significantly affected by the withdrawal of magic from the world, would there have been corresponding major changes in the magical community, leading to conflict with Muggles? There are a lot of potential answers to those questions, depending on perspective.

There could have even been radically different responses from different magical nations. Since this period involved the eventual emergence of Muggle Britain as the world's major imperial power, and at one point pitted almost all of continental Europe against the British, I could conceive of a conflict within the European magical community along similar lines. The complete collapse of the French monarchy and the Holy Roman Empire was a very different fate from the preservation and gradual reformation of the old order in Great Britain, suggesting two different approaches by wizards to Muggle affairs. Perhaps the continental wizards allowed Muggles to develop autonomously while British wizards sought to temper their revolution and maintain a haughty, manipulative control of events from behind the scenes.

 

I think one thing was not mentioned which could be a distinct possibility for conflict. In 1811 the current definition of a being has been laid out by Minister Grogan Stump. We know that for example the merpeople and centaurs were offered the status but refused. Furthermore, many people even during the time of the books still regarded some magical beings as lesser. It could be possible that such a "broad" definition of being, which included trolls, goblins, vampires and giants for example, led to an initial increase in tension between proponents of inclusion and opponents of it. This tension then could have boiled over till some people took actions by themselves. At the beginning they used one of the most viciously led war during the time as cover. I am talking about the Greek Revolution or Greek War of Independence, whichever name you prefer. With massacres on both sides it should have been easy to mask or hide other deaths.
The death of a major colony of centaurs leads to retaliation by them against muggles and the merpeople help in some way. These actions demand a response from the wizards, because their actions threaten the statute. This conflict could split the magical world in some way. Some people want to help the centaurs and merpeople against these vicious muggles and others just hope to deescalate the whole thing. Other groups agitate for more restrictive legislation or outright subjugation of these groups ,because they clearly lack reason.

The group ,who started all of this could have done it accidentally because they did not really have plan beyond killing magical beings or it was a plan to create a bigger platform for their agenda.

 

On Pottermore, Rowling mentions a ‘Country or Kind?’ debate during the American revolution. Given the Greek and Latin American wars of independence at the time, might wizards have been fighting in muggle wars? It is easy to see that this could have led the ICW decisively ban fighting in muggle wars, hence a 100 years of peace between muggles and wizards thereafter.