Deep space, the fifty-first century: the TARDIS arrives on the deck of a derelict spacecraft whose occupants have mysteriously vanished. The Doctor, Rose, and their newest traveling companion Mickey start to look around and make some curious discoveries, most especially of which is an antique French fireplace. Not just any fireplace, too, but one that seems to be anchored to some kind of space-time disturbance, for the Doctor looks inside and discovers the face of a little girl staring back at him. Her name is Reinette, and she is currently in eighteenth century Paris.
The Doctor trips a switch that twists the fireplace around and suddenly he's back in time, in Paris, along with the little girl, but several months have passed; the portal is out of sync, meaning that time goes by much faster on this end. Noticing that the clock above the mantelpiece is broken, but there is still a ticking noise in the room, the Doctor discovers a monster under the bed: in fact, an android, made of clockworks. But before he can examine it completely, the robot - which follows him back onto the spaceship - teleports itself away.
The Doctor returns through the fireplace portal, but it's over a decade later, and Reinette has now grown into an adult. Though he has only seen her as a child, Reinette has spent her entire life thinking about the mysterious man, and has obviously fallen for him. Before she leaves, she kisses him, and the Doctor discovers why he knows her - she is the Madame De Pompadour, mistress of Louis XV, King of France.
Back on the ship, Mickey and Rose make a frightening discovery - a human eye in a sensor, and a human heart beating in the middle of the ship's interior. The Doctor, meanwhile, discovers another portal, and a horse that has come through it; the portal leads to the exterior of the Palace of Versailles, where he spies Reinette and a friend strolling through the gardens. Later, the Doctor realizes that there are many 'gateways to history' aboard this craft - time windows, not to just any history, but Reinette's own, a fifty-first century spaceship stalking an eighteenth century woman. Through another window, the three go to Paris to rescue Reinette from another clockwork android, where they learn that while the robots are stalking her, they haven't done anything to her yet because she's 'not ready'. And they're after her because, as they say, they are 'the same'. The Doctor makes a mental link with Reinette (which she uses to see inside his mind as well as the reverse) in order to discover the truth as to why the clockworks are following her, but the only thing he really discovers is that she is in love with him.
On the ship, Rose and Mickey are taken prisoner by the clockwork androids, while the Doctor later returns apparently quite drunk, but in fact it's a ruse to shut the androids down. While it doesn't work, the Doctor learns that the clockworks are repair androids; they followed their instructions to the letter when the ship was damaged, salvaging parts first from the rest of the ship, and then the human crew itself, manifesting their bodies to keep the ship running. Now, they are convinced that Reinette is the last link to repairing their damaged craft.
Later, Rose steps through the portal to warn Reinette about the day she will be turn 37 years old, when she will be 'ready' and when they will attack. Reinette is ready, so that a few years hence, when the androids come again, she yells into the fireplace, calling the Doctor to her. Yet, for some reason, he does not come this time.
The time windows into the palace have been shut down by the clockwork androids before their attack, or so they think - the Doctor leaps in through another window on the back of the horse. He's also sealed up the windows as he's left, leaving the clockwork androids to realize that they no longer have a purpose since their window to the future, and their ship, is broken. The Doctor is stuck, back in time.
Later, though, Reinette makes a confession to him: the fireplace, the one that he originally spoke to her through, has been reconstructed in her bedroom... and the portal is still open, far enough from the disturbance that shut the others down. The Doctor goes back to the future, telling her that he will be right back... but forgetting the time variation, so that when he returns again, Reinette has died, and Louis XV and the Doctor watch as her hearse is carried away toward Paris.
The Doctor returns to the TARDIS to read a letter Reinette left for him, knowing he'd be back one day. Mickey and Rose ask why Reinette was so important to the androids, but the Doctor, his heart heavy with her death, says they'll probably never know. The TARDIS departs, its occupants unaware of the name of the ship, emblazoned on its outer hull: the SS Madame De Pompadour.
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