Depends on the time period.

As has been mentioned, Pan-European identity hadn't developed when the Turks came. In the heyday of the Ottoman Empire the Turks were seen as an invader, an other and a military and economic threat.

It was known that they came from the east, and they had taken their Empire by force.

It was known that they had more than once had the urge to push as far into Europe as they could, occupying areas up to Hungary, and southern Poland, and laying siege to Vienna and attempting naval campaigns to achieve superiority in the Mediterranean.

They were not part of Christendom.

It is a safe bet to say that the Europeans of the time, would have considered them an "other," and even among their own "us vs them" contests, would have put them on the outer egde of "thems," so to speak.

But later on, Post French Revolution, once the powers of Europe prefer the devils they know to the uncertainty and chaos of post revolutionary modernity, after centuries of co-existence, without renewed massive offensives into Europe, the Empire is dealt with differently. Although still an other, certainly, they were seen less as the dangerous eastern menace that killed the last vesitiges of Rome and more of the Empire next door. And they certainly were in Europe by then, to stay, whether they "belonged" there ethnically or not.

The Ottoman Empire used to be called "The sick, old man of Europe" so there is some tacit recognition of the Ottomans being at least partly European. The designation of European and non-European is open to interpretation even today and defies rationality; Russia is "European" but stretches all the way to the Pacific, while Turkey (who has applied several times for EU membership) is not. A huge part of this dichotomy is religious - even today - in that Europe is considered by many [even those in progressive countries like The Netherlands and Sweden] to be a Christian continent and the admission of a Muslim country into the European community is tantamount to blasphemy.

In the 19th century when England and France were divvying up mercantile and political spheres of influence in the Ottoman Empire, there was most definitely a sense that the Turks were some alien "other" - there are many diplomatic and not-so-diplomatic exchanges which reveal Europeans' superiority complex and Turks' "otherness" which might suggest that the difference is geographical....except for the favoring of Christians from further south and east by France and Britain. Armenians were not considered nearly as alien, nor were Greeks, Maronites, and Copts. Yet the Muslim Turk was.

In general, there was the political recognition that the Ottoman Empire was "European" in so far as owning territories in Europe, but they weren't considered culturally or ethnically "European" by the majority of Europe's peoples and governments.

For more information, see "Sources in the Middle East" by Ahram Khater

This is tough to answer. I feel like we could come up with a better question but I understand where you're coming from.

Most Europeans didn't consider themselves European at the time. That's a relatively recent phenomenon.

In short the Ottomans weren't part of Christendom. They had fundamental differences in terms of economy, government, institutions. Take for example the janissaries; whereas "European" armies of the time were made up of an aristocratic military class, men-at-arms, and mercenaries, the Ottomans formed a warrior class from converted Christian slaves. It was a force representative of an entirely different historical experience than the one "European" dynasties shared.

The geographic distinctions are arbitrary in some ways. Byzantine Asia Minor was part of that "European" - Christian - world. When the Turks conquered them, the fact that they held chunks of what we refer to as Europe didn't make them "European" to the rest of the continent.

I just read a biography of Suleiman the Magnificent and during his reign, post 1500, the Turks were seen as atrocious infidels. But I'm not sure what the perception of the European people was at other times in history.

Edit: Books name is " Suleiman the Magnifient: Scourge of Heaven" by Antony Bridge