Paris and Kim are taking the Flyer for a test flight... er, but Janeway used it in the last episode. Surely that was a test run? Another ship turns up and challenges them to a race to the other end of the asteroid field. Which is, astronomically speaking, improbably dense. The Flyer wins, of course, but the other ship suffers damage, and they have to beam the pilot out.
Meanwhile, Torres tries to persuade the HoloDoc to give up his Holodeck time so she and Paris can have a getaway. She guilts him into it. HoloDoc: "You haven't seen me in a bathing suit" (Noooooooooooo!!!!!)
Kim chats up the pilot, Irina, and she tells them she's entering a race. Paris and Kim therefore attempt to talk Janeway into letting them enter, and she says "smashing idea, chaps!" only not quite in those terms. So they set about modifying the Flyer to be race legal, and then Paris remembers that he and Torres has a romantic getaway planned. He warns the HoloDoc there may be a medical emergency and goes to tell Torres. She takes it amazingly well and then goes to sulk in the mess hall. She tells Neelix she doesn't think she and Paris are a good match, and he attempts some therapy. Does he have a licence to practice psychology? I think not.
Janeway sorts out the race entry, and arranges for the post-race ceremony to be held on Voyager, because the entering races are arguing over it. Paris talks to a somewhat anti-social pilot who's also entered in the race.
Torres catches Seven ploting race courses, and then they discuss Paris - then Torres volunteers to be Paris' co-pilot. Paris doesn't need much convinving,
Neelix interrupts Seven and starts doing the race commentating. Hey, the Moebius inversion looks exactly like the transwarp tunnel from the other season. Meanwhile, Paris and Torres have an argument because she thinks for herself too much. Then there's an accident and the race stops - Irina's co-pilot is badly injured, and Tuvok says it was sabotage. Tsk.
Kim volunteers to co-pilot for Irina. Paris and Torres bicker mildly some more. Kim is somewhat obviously fancying Irina. It's the pointy ears, huh?
The race restarts, but Torres is busy obsessing over Kim and Irina. Kim seems to be having problems helping Irina though... and then his console explodes and she pulls a gun on him. But he manages to get the gun off her, and finds she's disabled the comms system.
The Flyer rounds the last marker, but Paris and Torres are still bickering. Paris brings the Flyer to a halt so they can talk over their issues. Meanwhile, Irina seems worried because the Flyer has stopped. Kim starts putting 2 and 2 together and realises she's put a bomb on the Flyer.
On the Flyer, snogging is happening. There would be sexing now, but (a) Kim sends a morse message via a pulse, and (b) this is Trek, so no sex. Paris flies the Flyer into a nebula while proposing to Torres. They eject the warp core into the nebula and high-tail it out, though the Flyer becomes severely damaged.
Later, the pair get married and have a honeymoon in the Delta Flyer. Teh end.