How relieving to find out, then, that they're actually caught in the midst of the French Revolution!
Thankfully for Ian and Barbara, they've figured out the fine art of stroking the Doctor's ego. If they couldn't convince him to continue his historical investigations over a farewell pint of ale at the local pub, he might very well have abandoned them unknowingly in 18th century France. Such as it is, they find their way to a safehouse by which the aristocracy is fleeing the country, only to be captured by soldiers of the new republic themselves.
After this comes an adventure befitting the Scarlet Pimpernel, minus the costumed crusader himself. Between prison and plots and the ever-looming threat of the guillotine, the crew of the TARDIS are embroiled in the English spy network, the underground railroad of escaping aristocrats, and Napoleon Bonaparte's plan to overthrow Robespierre. The interpretation of the French Revolution is a fairly typical one, though interspersed with a modicum of nuance. As the plots unfold, Barbara becomes fond of one of the spies only to lose him later when he is shot in the attempt to capture Ian. As it turns out, her paramour was a counter-spy for the Republic and, grieving, she angrily lectures Ian on our inability to judge history. However, the line is clearly drawn between the anarchy of the revolutionaries and the goodness and honor of the counter-revolutionaries.
The Reign of Terror was the first of the Doctor's adventures to be set in the course of a particular historical event (if we don't count the taming of fire as a historical event). The pattern would persist when the TARDIS drops into the burning of Rome, the Trojan War, the St. Bartholemew's Eve massacre and the gunfight at the O.K. Corral. The only unfortunate thing is that this serial lacks a catch that was enjoyed by previous serials like Marco Polo and The Aztecs. It is a perfectly serviceable costume epic, though whether it had to be Doctor Who by name is another matter entirely. There are a few moments acknowledging the time travellers' foreknowledge, but otherwise it is The Scarlet Pimpernel.
Though this eighth story did not mark the end of the original filming block, the success of the show forced it into the position of the first season finale. Thus is was given the appropriate tweaks and nudges to bring things full circle: the extended theme of Ian and Barbara's quest to return home, and theme of the Reign of Terror itself. All the way back in An Unearthly Child, Susan exhibited her preternatural knowledge by criticizing a textbook on the Revolution. In the course of the show, she also reveals that this period is the Doctor's favorite in Earth's history.
Of course, they don't make it back home, though they do make it out of France with their heads still attached. Against a field of stars, Ian asks "What are we going to see and learn next, Doctor?"
"Well, unlike the old adage, my boy, our destiny is in the stars, so let's go and search for it..."