Rosenberg Academy

Sounds like an G dim chord to my ears, and not the C7b9b13 in the tab, both of which sound great.

G dim. C7b9b13
------------------------
--2----------------2---
--0----------------1---
--2----------------2---
--1----------------1---
------------------------

Am I right in thinking that the C7 is the V of the root key, but seeing that it is going to F+ (the V of This Lydian mode), the G dim makes more sense as a passing chord?

Yup, you're right. Mistake on my part. Stochelo is playing a dim chord (as does Django). The chord is an Edim which is VII for the dominant. I prefer not to think in modes in tonal pieces (as opposed to modal pieces). When chord progressions can be explained in normal functions (with extensions) I see no reason for modal analysis.