"A Bargain of Necessity" is pretty much an exercise in backing out of the plot cul-de-sac of the last episode. It does a good job of that, with some highly entertaining bits from Hartnell and some interesting moral debate from Ian and Barbara (and once again, Susan present as a plot anchor preventing the other characters from ditching), but you can still hear a faint beeping noise as the story goes through its motions.
The first chunk of the episode is mostly given over to Ian's interrogation and rescue, along with an explanation of the reveal that Leon is the traitor. It's one of those things that probably worked when the story was first shown but suffers greatly from the huge volume of guides to the series that collectively spoil Stirling's real identity. That is to say, the story has been working very hard to try to get the audience to believe that Leon is really Stirling, but if you know going in that he's not, then he by definition has to be the traitor because otherwise his character has no real purpose to the story. (This is also how Roger Ebert used to figure out who the traitor was in every action movie--he just looked for the person who would otherwise be utterly surplus to the plot.)
Ian's interrogation is played well--it's a scene that actually uses the overall flaw of the story as its strength, because this time the TARDIS crew is almost totally disconnected from events and has only the barest connection to the Stirling plot or indeed anything else. But Leon, who has been living in the world of espionage and plot and counter-plot and treason and counter-treason for years now, simply can't accept that Ian's motivation is nothing more than, "A dying man asked me to find a total stranger and give him a message, and I figured why not?" Because it's ludicrous. For the previous four parts, that's been the problem, but right now it creates a great deal of tension until Jules shows up to save the day.
Afterwards, we get one of those scenes that occasionally pops up in this era of the program and always, always, always works: Barbara confronts Ian and Jules with the moral complexity of the French Revolution and points out that no, Leon didn't "deserve to die" because he betrayed them...from Leon's point of view, they betrayed him and everyone he cared about. It's a great scene, made no less great because Barbara later apologizes; her apology isn't an acknowledgment that Leon did deserve his fate, only that there were no other alternatives.
Meanwhile, the Doctor is off being awesome. That's really all you can say about the scene where he tricks the jailer into letting Barbara go on the pretense that they can then follow her back to her confederates, only to explain after she leaves that he thought the jailer was going to do the actual following. Sheer poetry. After that, the brief look-in on the ostensible plot (Lemaitre is on to him, Robespierre is both terrified of betrayal and inexplicably absent-minded about the official change to the French calendar that abolished "July") is almost anti-climactic. Again, this story is very much a thing of parts in the absence of any real story, but that doesn't mean there's not a lot of enjoyment to be had from the best of those parts.