“What a cool town,” muttered Julian Casablancas, eyeing the pandemonium that greeted his arrival at Paris’s fittingly retro-classic grand hall L’Olympia. He was there for the second of this week’s three tiny, last-minute European shows by The Strokes. And what’s remarkable is that, seven years after their last album (2013’s Comedown Machine), nine since their last run of great singles (Under Cover of Darkness and Taken For a Fool in 2011) and almost 20 since their seminal 2001 debut Is This It inspired and defined the 21st-century generation of erudite guitar savages, they remain the undisputed arbiters of cult credibility.

They visit cool upon any room like a gaggle of Godard rebels. With bassist Nikolai Fraiture standing ankles-crossed in shades and baseball jacket, drummer Fabrizio Moretti hammering out locomotive beats in a pink Seventies lounge blazer, and Casablancas staggering around with half a haircut and the insouciant menace of a stoned mechanic who is definitely going to mess up your carburetor, they were equal parts The Breakfast Club, Mad Max, Swingers and Pulp Fiction.

“The 2010s, we took ’em off,” Casablancas told their Bernie Sanders rally in New York last week, but he sold The Strokes’ “wilderness” years short. Although the band splintered off to concentrate on side projects – notably guitarist Albert Hammond Jr’s solo albums and Casablancas’s psych rock band The Voidz – sporadic Strokes releases often saw them disown the 00s guitar pop wave they’d fathered and swerve into minimalist electronica, Thin Lizzy boogie and the pasty end of synth metal.