The correct answer is - Istanbul.
Istanbul is the largest non-capital city in Europe, but also the largest city even if the capitals in Europe are included. It has just over 15 million inhabitants, and its population is on a constant rise. Still, we have to take on notice that the city itself is not lying totally on European soil, but it is divided into roughly to equally large parts in both Europe and Asia.
If we go with a city that is 100% exclusively lying on European soil, than the biggest non-capital will be Saint Petersburg in Russia, with just over 5 million inhabitants.