Yes, where would we be without the rules-based international order? Perhaps we would be watching videos every day of children blown apart by weapons of war.
In Europe itself, you have quite major conflicts in the Franco-Prussian War, Austro-Prussian War, and the Crimean War, plus more minor conflicts around the unification (more like conquest) of Italy, the independence of various Balkan states from the Ottoman Empire starting with Greece, Prussia's war against Denmark. And then you have all of the internal civil wars or strife people usually don't call outright wars, but in the 19th century, were often quite violent. The Revolutions of 1848, for example. Or France switching governments four times (July Monarchy, Second Republic, Second Empire, Third Republic) after the restored monarchy, all of them quite violent transitions.
Not to mention the fact that the stresses of urbanization and concomitant social changes provoked a lot of resistance from the lower classes, which was often quite violent. It's not until well into the 20th century that major strikes don't involve lots of bloodshed!
19th century Europe is only peaceful relative to the quite bloody conflicts that bookended the time period, which themselves rank among the bloodiest conflicts in all of human history.
That adds up to about 5 years or less at war for almost all European countries. Probably the most peaceful century in the history of Europe.
During this time, European population also doubled, life expectancy increased by 10-15 years, and GDP/person more than doubled.
http://historyguy.com/major_wars_19th_century.htm
I'm sure there are others. It lists:
Greek War of Independence (1821-1832)
French invasion of Spain (1823)
Russo-Persian War (1826-1828)
Russo-Turkish War (1828-1829)
Hungarian Revolution and War of Independence (1848-1849)
First Schleswig War (1848-1851)
Wars of Italian Independence (1848–1866)
Crimean War (1854–1856)
Second Schleswig War (1864)
Austro-Prussian War (1866)
Franco-Prussian War (1870-1871)
Russo–Turkish War (1877–1878)
Serbo-Bulgarian War (1885)
Greco–Turkish War (1897)
Counting the years when there was a war anywhere is Europe, you'll end up with a large number.
I'm counting how often each country was at war. Several countries had no wars, and even the most war torn country didn't fight for more than 10-15 years.
Also not true of Spain, which spent a lot of time in internal warfare (with occasional outside interventions.)
But, yes, excluding those, most of the countries in Europe were too busy fighting endless wars throughout their (or their allies’ or enemies’) colonial empires (whether to expand them, defend them, or put down or assist rebellions in them) to bother fighting other powers in Europe in that period.
If, when you talk about "Europe", you exclude Spain and also Greece, the Balkans, and much of Eastern Europe, sure, the powers in "Europe" did most off their fighting in colonial wars in the period rather than at home (they did a quite a lot of fighting in colonial wars, though.)
Danish vs Austri-Hungary and Prussia 1864.
Belgian Independence 1831
Civil Wars in SPain 9Carlist War) and Portugal 1830s
Revolutions of 1848
No, absolutely not. This is factually incorrect.