***This synopsis has errors and timeframe issues. I'm in the process of correcting those and giving more detail to it, much of which I've already done. This is my favorite Bogart movie of all, and with all due respect to the original writer, I'm not completely re-writing it, but simply organizing it sequentially. I will have it completed in the next few days as time allows me.***
Harry Morgan (Humphrey Bogart) and his sidekick Eddie (Walter Brennan) run a charter fishing boat in Martinique (controlled by the French government at Vichy, which in turn was Nazi-controlled after 1940). Their current client is an American fisherman named Johnson who grudgingly pulls out money to pay for gasoline for the boat, and who then ineptly loses two large marlins by not following Harry's orders. The second loss also includes all the tackle he was using. He tells Harry he is leaving Martinique in the morning and will pay him after he goes to the bank in the morning, because he doesn't have enough money on him.
Back at the hotel, Gerard (Frenchy), who is the hotel owner and a member of the Free French resistance, comes to Harry's room and asks him to take on a smuggling job for the Free French Resistance movement. Suddenly a sultry young woman (Lauren Bacall) appears in his doorway asking for a match. Harry tosses her a box of matches and she leaves. Harry asks Frenchy who she is, and he says she came that afternoon on the plane from the south. Harry tells Frenchy he doesn't want any part of the movement or their activities.
Later in the dining room he notices Marie with his American client, who acts too fresh for her taste. She brushes him off and goes to stand by the piano, where Cricket (Hoagy Carmichael) is playing and singing "Am I Blue?" She joins him in the verse and they harmonize well. Harry sees Marie pick up Johnson's wallet and leave the room. Frenchy stops at Harry's table and tells him he hasn't been able to head off the men who want to hire Harry's boat for the smuggling operation, and Harry tells him he'd better head them off. Harry follows Marie upstairs and stops her as she's entering her own room and makes her come with him into his room. He makes her hand over the wallet and finds it's full of traveller's checks and cash, enough to pay his bill, along with a plane reservation for earlier the next morning than Johnson had said he'd meet Harry to pay him. Harry is glad Slim (as he calls her), took the wallet and didn't return it after all. She says she needed money to leave Martinique.
Frenchy comes to the door with his group of comrades who offer to pay Harry to pick up two people secretly from another Caribbean island and bring them back to Martinique. Eddie comes in during this business and asks the French resistance leader if he was ever stung by a dead bee. The man tries to shut Eddie up, but Slim takes up the question seriously, delighting Eddie and getting Harry's approval. Eddie leaves with a coin for a drink. Harry refuses to get involved, despite their pleadings. He leaves the room, taking Slim downstairs with him to confront Johnson and return his wallet and ask for the payment Johnson owes Harry. As Johnson is about to sign over the traveller's checks, the pro-Nazi French police open fire in the lounge at the resistance group that had come down from Harry's room, and Johnson gets killed by a stray bullet.
Capt. M. Renard (Dan Seymour), the head of the local Gestapo, closes the hotel lounge and picks out four people for questioning--Frenchy, Harry, and Slim being three of the four. At the station, they confiscate Harry's money and passport and question everyone. Harry gets riled at the methods of questioning and fights back, then grabs Slim and tells her, "Let's get out of here," which they do.
Harry and Slim end up going to another bar, but they realize neither has any money, so Slim asks Harry if she should do her thing, and he says, "Go right ahead." She immediately turns on the flirtatious charm with a French officer there, and he gets up and starts dancing with her. Harry leaves, grinning. He knows she's "good" at what she does, but it begins to bother him.
Later, she comes to his room with a bottle she has presumably charmed out of the man she was with, but Harry's reaction makes her feel cheap and she leaves, angry. He follows her across the hall to her room and they have it out. They have their first kiss, then another and, as she's leaving his room, she tells him to whistle if he needs anything. "You know how to whistle, don't you Steve? You just put your lips together and . . . blow." She shuts the door and he lets out a low wolf whistle.
His American client dead without paying him, the rest of his money confiscated by the police, having refused Slim's last few dollars, Harry reluctantly takes the smuggling job. He's supposed to pick up the two Frenchmen from another island and deliver them back to Martinique in the middle of the night. He makes them pay him in advance, and he arranges a plane ticket for Slim for that afternoon to fly back to her home.
Harry doesn't want to take Eddie with him into danger so he insults and slaps Eddie to keep him on shore while he goes out to pick up the Frenchmen. Eddie tricks him and smuggles himself aboard. Eddie comes out of hiding and confronts Harry, telling him he knew it was all a lie. Together they pick up their cargo which turns out to be a man and his wife, Paul and Hellene de Bursac (Walter Molnar and Dolores Moran). On the way back to Martinique they encounter a patrol boat and the Frenchman takes one in the shoulder. Harry shoots out the patrol boat's spotlight, and they head back to their destination in the foggy night waters.
Harry and Eddie get the Frenchman and his wife back to Martinique. They find that Slim intentionally missed the plane home and has been hired to sing with Cricket and his combo. She helps Harry remove the bullet from de Bursac's shoulder while his wife makes demands and has hysterics and finally faints. Slim keeps her cool but is pointedly jealous of Madam de Bursac's flirting with Harry, and Harry's obvious response to her.
Captain Renard tries to get Eddie drunk to find out where the Frenchman and his wife are. Harry intervenes and breaks up the questioning. It turns out that de Bursac is actually supposed to get a resistance leader off Devil's Island to help the cause, and he wishes he had Harry's courage. Soon afterward, Captain Renard again gets hold of Eddie, and tries to blackmail Harry into giving over the location of the Frenchman by threatening to withhold liquor from Eddie to make him go into delirium tremens and crack up. Harry gets a gun from his desk drawer and shoots one of Renard's henchmen and handcuffs the other and Renard. He beats them both until they agree to make the arrangements so that the de Bursacs, Harry, Eddie, and Slim can all leave the island for good.
With everything fixed up, they gather in the hotel lounge where Slim wins over Eddie when she asks him, "Was you ever stung by a dead bee?" Eddie says she's all right and she goes over to say goodbye to Cricket who's playing piano. He asks her if she's happy, and Slim says "What do you think?" doing a dance back over to her "Steve."