Firstly, this is a very dated film, non-focused in its exposition of the left wing political revolution. Honestly, when someone says that the only way to be truly revolutionary is to cease to be intellectual ( which in itself is quite nonsensical, since the answer was arrived at by precisely being intellectual) it reduces me to despair; as if we all should return to being apes in the name of equality - it is simply ridiculous. Our intellectuality is only one of many human qualities, but this does not mean we should not educate ourselves to the highest possible degree. But no doubt this non-educational message ties in with Godard's use of rock music; hence The Rolling Stones.
The song 'Sympathy for the Devil', whose creation we witness, and from which the film takes its name, is in fact nothing special. The chord sequence, which is not especially original, was used to much better effect in Led Zeppelin's 'Thankyou'(Led Zeppelin II). Apart form that, 'Sir' Mick Jagger declaims in his usually nebulous manner (rather like Bob Dylan)- notice how the first melodic phrase is unimaginatively repeated over again to form the verse.
Besides the fact that the Black Panthers depicted in this film, don't seem to know what they are fighting for, the most interesting scenes involve the equation of fascism with pornography; a message that in fact undermines the sexual 'liberation' of the 1960s and today ( indeed, a message that would belie the behaviour of The Rolling Stones around the time the film was made).
No wonder, the DVD came free with The Sunday Times! For a truly profound historical exposition of left-wing sympathy, listen to Luigi Nono's masterpiece, 'Al Gran Sole carico'd'amore'.