"Return" to whom. Byzantium was never "European", it was shunned at its time by entire Europe - by both the Catholic Mediterranean parts and the Germanic parts. The Romaioi (as the Byzantines called themselves) turned into Ottoman Rums as the empire was a multi-cultural, multi-national empire united under the banner of Ottoman-ness. The uncle of the fallen emperor, who was next in line for being the Byzantine emperor after the fall of his nephew was made the "Grand Beg" (akin to viceroy) of the entire Ottoman Balkans after the fall of Constantinople. He governed lands far bigger than what his ancestors governed even ~200 years ago. A lot of Mehmed I's begs were ex-Byzantines who were still Christian, and, well Byzantine. Except they wore Ottoman turbans now - and most of them just didn't and kept wearing Byzantine attire.

So its like what some historians say: The fall of Constantinople was mostly a change of hats.