Paul has forgotten the Bach piece's title, but many fans and scholars have assumed it's the Bourrée from his E Minor Lute Suite, BWV 996.
Perhaps score study will yield results.
As it turns out, no, it is the Bourrée. Paul might not know the name of it, but he can still play it, and on 28 July 2005, Paul performed a live solo concert at Abbey Road Studios, which was recorded and released as Chaos and Creation at Abbey Road. During the performance, he again cited Bach as an influence on "Blackbird" and even played a few measures of the Bach original to illustrate the similarities (which can be heard from about 37:39-38:51 in the video below).
Miles, Barry. Paul McCartney: Many Years From Now. Henry Holt and Company Inc., New York, NY 1997.