I like to keep Wikipedia handy when reading this manga.
So this chapter is happening between 16 October 1793 (execution of Marie Antoinette, FRC: 25 Vendémiaire, Year II) and 13 March of the next year (arrest of Hébert, FRC: 23 Ventôse, Year II).
At this time, Napoleon was still at Toulon, as the city wouldn't fall until the 19 December 1793 (29 Frimaire)
We see a couple old faces in this chapter, as well as a couple new ones. Starting from the less consequential ones:
Marie Antoinette, former Queen of France, executed at the beginning.
Jacques-Louis David is the man sketching Marie in the beginning, the manga is actually taking an artistic license with his character, as he was already a well established artist before the Revolution (for example, Oath of the Horatii is from 1784), and his high status came from being a friend of Robespierre's.
And then the three central figures of the upcoming arc it would seem, in order of executions (all Montagnards):
Jacques Rene Hébert (15 November 1757 - 24 March 1797 [4 Germinal, Year II]), editor of the radical newspaper Le Père Duchesne (fr: Old Man Duchesne), representative of the radical wing of the party, and the interests of the sans-culottes, the urban poor.
Georges Danton (26 October 1759 - 5 April 1794 [16 Germinal, Year II]), lawyer, former president of the National Convention, revolutionary Minister of Justice and a founding member of the Committee of Public Safety (guys behind the Reign of Terror), representing the moderates.
Maximilien François Marie Isidore de Robespierre (6 May 1758 - 10 Thermidor, Year II [28 July 1794]) one of the leading figures of the Great Revolution, Robespierre was behind the downfall of the monarchy, the creation of the National Convention, as well as the architect of the Reign of Terror. A very controversial figure.
So, what exactly is happening here? Long story short, there was this party called the Jacobins, which was behind the abolition of monarchy in France is favour of a Republic during the Revolution (they didn't cause the Revolution itself, they were just one of the movements in it)
The Jacobins split after the dethronement of Louis XVI into moderate Girondins and radical Montagnards (The Mountain). We have seen in the earlier chapters the assassination of Montagnard Jean-Paul Marat by Charlotte Corday. The assassination was the aftermath of the destruction of Girondins in early 1793.
But as always, when the external enemy is defeated, the revolution starts devouring its own children, so the Montagnards themselves split into radicals and moderates.
Robespierre wants to keep the government on track, but the infighting make it difficult. The Hébertists are the voice of the very radical sans-culottes, the urban poor of Paris, who were supporters of the Jacobins since the beginning. (Also, that stuff about falsely accusing the Queen of incest? That's true. Robespierre even called Hébert an imbecile in response) Meanwhile Danton leads the more moderate wing.
It looks like the upcoming arc will be about the infighting of The Mountain, the destruction of Hébertists, execution of Danton and the eventual Thermidorian Reaction and downfall of Robespierre.
How does Napoleon fit into all this?
Well, his military commission came thanks to his connections to one Augustine Robespierre, Maximilien's brother. So Napoleon will have a lot of trouble due to his connections to the radicals in power.
EDIT: Some stylistic mistakes and the timeline around Marat's death.