What is the biggest business directory in Europe? For example, in North America, Yellow Pages is pretty much the biggest and most refined business directory. What about in Europe?
There isn't one. Each country has their own.
Many of the dominant ones are "Yellow Pages" of some kind (the trademark was licensed widely) but not all. Some have Yellow Pages and other competing directories that are widely used at the same time.
As a general comment - if you're coming into a European market from the US it's pretty much always wrong to think of it as "Europe". You need to think of UK, France, Germany, etc. Treating Europe as a single market because of the EU is kind of like treating USA & Mexico as a single market because of NAFTA. It makes trade easier and provides some legislative commonalities - but they're still different countries.
You could try Opendi: http://www.opendi.com/
It's more or less what come next to what you have asked.
As others pointed out, there are yellow pages, they are just for every country and not combined.