I have watched many clips of Django Reinhardt and Stéphane Grappelli playing together on the Classic Arts Showcase channel, and I've never seen him use his left thumb. I'm not saying that he didn't, but I've never seen him do it.

He was severely burned in a fire when he was 19 years old, almost lost a leg, and lost the use of the ring-finger and little finger of his left hand. He worked out a way to play rhythm guitar using just his first and second fingers. His method was to play the basic notes of a chord with his two good fingers (often not playing a complete chord), and position his hand in such a way that he dampened the strings that were not in the chord.

Jazz guitarists often do this damping thing, and I once had a jazz guitarist show me how this was done. Although he swept his pick across all six strings, his fingers were angled low over the strings so that the strings he didn't want were dampened, producing only a "fump" sound. Percussive rather than harmonic. In this position (the position I've seen Reinhardt use), it would be next to impossible to wrap his thumb around the neck to fret a bass string.

Don Firth