While there are plenty other who may exceed in certain segments of culture, none reaches the extent and class of Paris.
Best contenders as 'capital': a) Florence, cause it's sort of what most European cities would aspire to be - culturally, and b) London, though it doesn't identify as European.
Yes, it has been a longstanding tradition to call Paris the cultural capital of Europe. Even though there are many culturally prominent cities in Europe, it's clear that Paris is among the most popular. It certainly does have a lot of great cultural and architectural offerings, including the Eiffel Tower, the Louvre, Notre Dame, l'Arc de Triumph, and so many other cultural icons.
Being not from Europe, it's hard for me to say. However, I can say for those who do not live there, Paris is probably the most well recognized city. It is also most likely the most visited city for tourism. To me, that would make it a pretty safe bet for the unofficial cultural capital of Europe.
Paris has so much culture that no other city can equal. They have that famous art museum. They have the beautiful river that runes through the city. They have all of the locks that people place all over the city to symbolize their love. They have delicious food. Paris is where all of the culture is in Europe.
Paris, is without a doubt one of the culture capitals of the world, but Europe has so much diversity of offer that it's unfair to name Paris as it's one and true culture capital. Rome, Berlin, London all are equally important to the world culture. I guess it all depends on what you identify with the most,