According to William Friedkin, the significance of the straw hat being tossed onto the shelf of the rear window in Doyle and Russo's car was that at that time it was a universal signal in the New York City Police Dept. that there were undercover cops in the car, on duty.
The early scene where Doyle and Russo chase down a drug dealer while Doyle is dressed in a Santa Claus suit, is based on a real-life tactic used by Eddie Egan and Sonny Grosso. While on stakeouts in Bedford-Stuyvesant, Egan and Grosso discovered drug dealers could easily spot undercover cops, and they would often flee the scene before the cops could arrest them. One Christmas, Egan came up with the idea of dressing in a Santa Claus suit, figuring the dealers would never suspect Santa Claus of being a cop. As depicted in the film, Egan walked the neighborhood streets as Santa Claus, singing Christmas carols with local kids. When he saw a drug deal going down, Egan sang "Jingle Bells" as a signal to his partners to move in and make the arrest. The tactic worked beautifully, and Egan and his partners made dozens of Christmas arrests over several years.
The car chase was filmed without obtaining the proper permits from the city. Members of the NYPD's tactical force helped control traffic. But most of the control was achieved by the assistant directors with the help of off-duty NYPD officers, many of whom had been involved in the actual case. The assistant directors, under the supervision of Terence A. Donnelly, cleared traffic for approximately five blocks in each direction. Permission was given to literally control the traffic signals on those streets where they ran the chase car. Even so, in many instances, they illegally continued the chase into sections with no traffic control, where they actually had to evade real traffic and pedestrians. Many of the (near) collisions in the movie were therefore real and not planned (with the exception of the near-miss of the lady with the baby carriage, which was carefully rehearsed). A flashing police light was placed on top of the car to warn bystanders. A camera was mounted on the car's bumper for the shots from the car's point-of-view. Hackman did some of the driving but the extremely dangerous stunts were performed by Bill Hickman, with Friedkin filming from the backseat. Friedkin operated the camera himself because the other camera operators were married with children and he was not.
Roy Scheider and Gene Hackman patrolled with Eddie Egan and Sonny Grosso for a month to get the feel of the characters. Hackman became disgusted at the sights he saw during this patrol. In one incident he had to help restrain a suspect in the squad car and later worried that he would be sued for impersonating a policeman.
The scene where Doyle and Russo chase down the dealer near the beginning and Gene Hackman shouts out his famous question "Did you ever pick your feet in Poughkeepsie?" is based on actual "good cop/bad cop" interrogations by the real "French Connection" detectives, Eddie Egan and Sonny Grosso according to William Friedkin in the DVD commentary. Grosso would gingerly ask a suspect direct questions about his crimes, then Egan would always butt in and yell unusual questions like the Poughkeepsie one. The suspect would get so rattled by Egan's offbeat questioning that he felt more comfortable answering Grosso's, thus tending to eventually incriminate himself.
Eddie Egan, Sonny Grosso: the real-life models of Doyle and Russo appear in the movie: Egan as the detectives' supervisor, and Grosso as Klein, the BNDD Special Agent, Mulderig's partner.