On one hand, a sequel to The French Connection is completely logical. Popeye Doyle sees things through, probably more out of psychosis than out of any loyalty to law and order, and so it does make sense that he’d track the kingpin Alain Charnier all the way to Marseilles after the events of the first film. French Connection II begins right there, not long after the first film left off, and when he pulls up in a cab it’s pretty great to see Popeye again. He pulls his hat onto his head and pays the driver, then glares at him when the driver shakes his head and insists he’s owed more. “I’m taking your number, fella — that’s in case you screwed me,” he snarls. Yes: it’s Popeye.
On the other hand, though, a sequel to the perfectly imperfect conclusion of the first film seems simultaneously illogical. The first Connection ends somewhat suddenly when Popeye accidentally shoots a fellow cop, thinking him to be the evasive Charnier (or “Frog One”). Not only is a wishy-washy ending avoided, but Popeye’s character is further complicated by the brevity of his victory. The smarmy sarcastic wave that Popeye gives Frog One on the bridge is bittersweet, and maybe even a karmic contributor to the ultimate conclusion of Connection (in the same way that Hank’s wave to Walt in Breaking Bad represents his own short-lived supremacy).