Assuming the setting is historical Japan, a European longsword will shred katanas in combat.
I know I’m going to irk the Kendo practitioners with this, but when you compare Kendo and German School Fencing, Kendo is a much slower form.
(And, before someone chews me out for this, I’ll say again, what I said six months ago, “a katana isn’t slow for a katana, it’s slow for a sword.”)
The katana needs to be wielded with finesse to protect the blade. In theory this is true of a European sword, but non-Japanese blades are (generally) a lot more durable. European fencing will call for you to do things with the blade that a katana just can’t survive.
The reason for this is usually simple metallurgy. Historically Japan, never had access to large supplies of high quality iron, the iron they forged the katana from would have been discarded as scrap in most of the world after the eleventh century. The blade was folded to bring the carbon content down into a manageable range, but the result was (in comparison to sword technology elsewhere) fragile.
If your setting is fantasy, then they might have access to the same metallurgical resources as your fencer, meaning they could produce weapons that would not shatter in combat. But, if that’s the case, the katana design isn’t likely to emerge.
It’s possible the original katanas were copies of the Chinese zhanmadao. Both date to the 12th century, and share an obvious visual similarity. The difference was the zhanmadao was intended as an anti-cavalry sword, and was roughly twice the size. If you want to run with that, then you’d be looking at a setting where katanas were wielded against mounted combatants.
The other possibility is, if your fantasy Japan doesn’t suffer from the metallurgical problems the real one did, that their martial style would change drastically.
I’ve seen non-Japanese alloy katanas used in an approximation of saber and cutlass styles. It isn’t ideal, but it does make the katana into a much more effective weapon, when dealing with a German School combatant. Depending on your setting, you might want to push that approach over traditional Kendo.
The other major option is jumping straight over to Chinese weapons like the Jian and Dao. Youtube has some fantastic Dao forms from modern Wushu. This can help keep the intended exotic tone of the setting, without devolving into orientalism. (And as always, take a look at Edward Said’s book, Orientalism, for a long list of things you probably want to avoid.)