We can't be sure to credit democracy for this and not say most of the continent being part of the same military alliance or common market.

Sure, and we can't rule out the sheer risk of nuclear war, or anthropic issues (if every European war quickly escalates into nuclear war we might have a serious survivorship bias). Also it is possible that stronger taboos have simply made war less acceptable (although that might be due to democracy in part),.

Long periods of relative peace are hardly unpredcedented in European history.

The Concert of Europe is an interesting example to some extent as to how different the post World War II Western Europe looks from that. You had for example a large number of civil wars and revolutions, as well as proxy conflicts outside Europe and then outright wars like the Schleswig wars and the Franco-Prussian war. In contrast, there have been zero wars in Western Europe post-1945, whether civil wars, external wars, or proxy conflicts among the Western European powers. Moreover, much of the lack of war during the Concert is attributable to a drop in the number of conflicts between France and Britain which in that time period had become functioning democracies.