Carmine Falcone was Gotham's most untouchable gangster, who built his syndicate from the ground up. After he befriended Thomas Wayne at some point, Carmine often visited him and had injuries that he had sustained treated. When he took control of Gotham's organized crime, Falcone let Thomas deal with his money laundering and "befriended" Mayor Hamilton Hill, to help deal with the politics in the city. With control over the main areas of Gotham, the three became the city's most powerful crime lords, though the Waynes appeared less so than Falcone and Hill. Falcone also may have had an addiction to Morphine, though he managed to kick it for forty years before the game's events.
The group also collected large amounts of psychogenic chemicals, which they used to declare people who got in their way insane. With that, they committed many people to Arkham Asylum and, using all their resources, took control of what was previously out of reach. Falcone also kept barrels of that chemical in a warehouse in the East End, making sure nothing could be traced to Hill and the Waynes.
After the deaths of Thomas and his wife, Martha, at the hands of one of his hitmen, Carmine began to build up his own businesses as fronts. It's possible that he knew that Hill had hired Chill to kill the Waynes, which caused some adversity. Falcone also ordered his men to place white roses, the organization's symbol, at crime scenes, to let his rivals know that he was responsible and as a fear tactic for the uncorrupted people of Gotham.
Falcone first appeared at Harvey Dent's fundraiser at Wayne Manor. Carmine and several of his henchmen examined the manor, with him voicing his interest in buying it. He was greeted by Dent and Bruce Wayne, whom came to meet. At Alfred Pennyworth's suggestion, the group went to the parlor to discuss their businesses in private. Bruce could also request that Harvey attend the meeting, despite Falcone's protests.
Falcone explained his concerns over Dent's policies and plans for the city, which Bruce either defended, sided with him on, or said that both could be done simultaneously. Carmine continued to explain that he didn't come to talk to him about politics, but to have him join the organization. If Bruce refused, Carmine tried to explain about Thomas's past dealings with him and the organizations that he ran. Here, the player was given a choice:
Bruce accepts Carmine's offer and he leaves in good spirits. He also decides not to buy the house, commenting that he deserves it.
Bruce either tells him to leave or not to talk about his father in such a way. Falcone, angered leaves, commenting that he's no longer interested in the house, insulting him and saying that "he'll get what's coming to him".
The next evening, Batman assaulted the Skyline Club, hoping to capture Falcone and interrogate him over an incident at the Docks earlier. After Batman took down six of his own henchmen, him retaliated by opening fire at him, though two of his men were caught in the crossfire and killed. Batman, using his Grapple Gun, destroyed the floor below him and forced him to flee to his office. Using the security camera feed, Falcone tried to shoot at Batman, but the system was disrupted by an EMP Mine and Batman successfully broke into his office. After a further scuffle, he activated a mini-gun that he had hidden, though it and the window were destroyed by one of Batman's drones. Batman demanded that Falcone tell him about the Docks and the chemicals, but Carmine stated that he owned the building and the chemicals, though he had nothing to do with the incident that went on there. What happens to Falcone depends on the choice made.
Batman impales Falcone on one of the metal rods dislodged in the explosion. Demanding that he talks, he reveals that the Wayne family did have ties to him and his organization. Falcone is later taken off the rod and arrested by the GCPD after Batman leaves.
Batman places Falcone in bonds and hangs him from the window. Demanding that he talks, he reveals that the Wayne family did have ties to him and his organization, before being left for the cops by the vigilante.
Following his arrest, Falcone was placed into medical care by the GCPD. After he began to suspect that the crime lord may have had a hand in his parent's murder, Bruce decided to talk to him and learn the reasons why they were killed. Due to the evidence handed over to Vicki Vale or Lt. James Gordon, Falcone was only visited by officers assigned to protect him. However, using all of the political ties that they could gather, Bruce and Harvey managed to buy some time for the former to spend in his company.
Falcone was surprised to see that Bruce had come to see him and confirmed his father's affiliation with him and the organization. He continued to explain that he, Thomas, and Hill had run the city and that he considered the Waynes as family. However, before he could explain the predicament, Falcone asked Bruce to reduce the pain that he was in with some Morphine. The player then had the option to give it to Carmine or cause more pain:
Bruce gives Falcone a small dose of Morphine, reducing the pain. Carmine asks what Bruce is and thanks him for the act, commenting that the act reminds him of Martha Wayne.
Bruce strangles Falcone, demanding that he tells him the truth. When he finishes, Falcone comments that this behavior is the reason why he was kept in the dark. He also states that it reminds him of Thomas, due to the ruthlessness, though states it is the reason why he, Hill and Bruce have their current wealth.
When Bruce finally asked about his parents deaths, Falcone revealed that he had no part in Thomas and Martha's assassination. When Bruce asked who did, Carmine commented that Gotham didn't have some of the most trustworthy people, especially friends. However, before he could tell Bruce more, Falcone was gunned down by Renee Montoya, who is revealed to be drugged by one of the Children of Arkham.
Falcone's death caused massive controversy about the GCPD and a massive power vacuum within Gotham's Underworld. That also gave the Children of Arkham, the group that had organized Carmine's death, a large amount of confidence as they began regular attacks on Gotham and its supposedly corrupted, most notably Hill and Bruce. Alfred also recounted Falcone's death as ironic as he was killed by the very chemical that he used in his operations.
Penguin, whilst in control of Wayne Enterprises, would also try to buy an island, planning to name it "Falcone Island" out of possible irony. Lady Arkham, who helped arrange Falcone's death, would also cite his and Hill's as a reason why she had helped Gotham, something which Batman disagreed on. When Amanda Waller arrived in Gotham, she commented on how she admired Batman's treatment, but commented that he could have gone further.
Falcone seemed to act civilized and calm around others, but this only masked his brutality and willingness to destroy the lives of others. Though he showed signs of aggression and violence, often resorting to it as one of the first options. His hunger for power also lead to him becoming territorial, though he was unwilling to betray those closest to him.
When Batman attacked him at the Skyline Club, Falcone used a machine gun in an attempt to kill the vigilante. It's unknown whether this was the firearm he used in other conflicts or deployed during attacks on the club. He also seemed to use ammunition capable of breaking through objects, such as walls and armored doors.
Falcone kept a sentry gun hidden within his office at the Skyline Club, which he would deploy whenever someone attacked his office. The activator was attached to his white rose button, which he would wear on his suits. During Batman's assault on the business, Falcone deployed the weapon, only for it to be destroyed when Batman deployed a missile barrage from one of his drones.
Thomas and Martha Wayne
Falcone and "Tommy", as the former seemed to call him, were partners in crime, and worked with Mayor Hill to secure three important spots in controlling Gotham. Falcone may have been around to take the fall for Wayne and Hill, as he was the only person whose criminal background was known by the public. Before he was murdered, Thomas believed that Falcone had hired Chill to take the hit. It is implied that Falcone may have had an affair with Martha, due to him saying to Bruce that she "had the human touch" and how he "only had good things to say about her".