(1/3) My favorite story about the making of The French Connection is that when they asked the New York Transit Authority how much it would cost for them to crash a subway train on screen, the official they asked instantly replied: $50k.
Director William Friedkin was surprised that he came up with a figure so quickly and asked how he did it. The official (who was Jamaican) said that if he authorized the crash he'd be fired and have to return to Jamaica to avoid arrest. $50k would buy him a comfortable life.
Friedkin provided the $50k. The official authorized the crash and then fled to Jamaica where he was never heard from again. The result is one of the greatest car chases of all time (which has another great story behind it).
The car chase story is this: In order to film as exciting of a car chase as possible (and because the alternative would be too expensive), Friedkin decided to shoot the film's climatic chase scene by simply having a stunt driver race through normal NYC traffic, without warning.
This was extremely dangerous and illegal, so it was shot with just the stunt driver and Friedkin in the passenger seat with the camera. The first time they attempted it, things went pretty well: they swerved through NYC traffic at high speed without getting arrested.
Friedkin knew the run could have been more exciting, though. So as soon as he got out of the car on the first attempt, he loudly demanded "a driver who isn't a pussy." The stunt driver demanded that Friedkin get back in the car and went all out. That run made it into the movie.