It was easy enough to find out the name of the pianist. It would appear to be Jean-Joel Barbier. All I did was Google "Schubert Au Hasard Balthazar Robert Bresson" and the first item that came up was THIS. It contains the following text:
"The credit sequence of Au Hasard, Balthazar remains one of the most startling in film history. Against a grey backdrop, the titles appear: the cast, the credits, the title, all in lower-case letters. This is accompanied by Jean-Joel Barbier's rendition of Schubert's Piano Sonata No. 20."I then looked up Barbier but could not find any source for a CD/record in which he plays this piece by Schubert. I had not previously heard of Barbier. He would appear to be a rather minor character on the piano scene, and as far as I know he is not a noted Schubert interpretor.
I have listened to the piece on the video and compared it with several versions I have. I would reckon that the closest in style/speed is the version by Elisabeth Leonskaja, who is an excellent pianist and a very good Schubert interpretor. You can buy MP3 tracks of her version of Schubert's Piano Sonata No 20 at Amazon HERE. If you want all four movenents of this sonata you need item numbers 30, 57, 36, 39. (For some peculiar reason known only to Amazon, these numbers are all over the place, and not adjacent as one might expect). But if you want only the second movement (as played in the video) you want item 57. You can listen to the first minute of the piece by clicking on the item.
Apart from Sonata No 20, may I recommend that you explore other Schubert piano sonatas. The last three, nos 19-21, were written during the last year of his short life, and they are perhaps his most well known. But some of the earlier ones (especially Nos 11-18) are quite magnificent too. One of my favourites is No 18, and I am pretty sure you would be impressed by that one, especially the second movement "Andante". For this sonata, I would recommend the version by Maria-Joao Pires. Generally speaking, other excellent Schubert pianists whom I like are Brendel, Richter, Imogen Cooper.