Here is the explications you could read below the video (very interesting):
The much beloved Ave Maria by Charles Gounod has a curious history: it is in fact the work of two composers. What I play on the keyboard is Prelude no. 1 of the Well-Tempered Clavier by J.S. Bach. This piece was composed in 1722, and Gounod, 130 years later, heard it, was fascinated, and composed a lovely melody over the sequence of broken chords. According to my sources, it was in fact his future father-in-law who heard Gounod play his improvisation and decided to write it down and create an arrangement for violin. Later, it was arranged for voice, with the Ave Maria as the text. Only one additional measure is added by Gounod, to heighten the drama of the repeated "Maria!". In this video we are performing the piece as an encore.