The Doctor, Ian, Barbara and Susan arrive in the TARDIS on board aspaceship. Their initial concern is for the ship's human crew, who are suffering from telepathic interference from the Sensorites, but Susan communicates with the Sensorites and finds the aliens fear an attack by the humans and are just defending themselves. Travelling to the Sense Sphere (the Sensorites' planet) the Doctor seeks to cure an illness to which the Sensorites and Ian have succumbed, but finds it has been caused by deliberate poisoning. The political manoeuvring of the Sensorite City Administrator poses another threat to the TARDIS crew as he seeks to discredit and implicate them.

The TARDIS materialises not far from Paris in 1794 — one of the bloodiest years following the French Revolution of 1789. The travellers become involved with an escape chain rescuing prisoners from the guillotine and get caught up in the machinations of an English undercover spy, James Stirling — alias Lemaitre, governor of the Conciergerie prison.