Short answers, pulled from the story.
The French First Republic was founded on the 21st of September 1792, when the National Convention voted unanimously to abolish France's constitutional monarchy. The republic lasted until the 18th of May 1804, when Napoleon Bonaparte was proclaimed Emperor of the French.
The September Massacres occurred in the first week of September 1792, when Parisian mobs broke into the city's prisons and killed over half the inmates, including nobles, clergymen, political prisoners, and common criminals. The massacres took place weeks before the National Convention declared the French First Republic on the 21st of September 1792.
The Reign of Terror was a period of the French First Republic when the Committee of Public Safety, created on the 6th of April 1793, executed perceived enemies of the republic by guillotine at an ever-increasing rate. The Committee had been established to address uprisings in the Vendée and Brittany, food shortages, military defeats, and the desertion of the army's commanding general.
Louis XVI was convicted of high treason on the 16th of January 1793 and executed five days later, on the 21st of January. The National Convention stripped him of all political powers at its first session and had put him on trial starting in December 1792.
The Directory, formally established on the 3rd of November 1795, governed France through a bicameral Parliament and a collective executive of five directors. The Parliament consisted of the Council of Elders with 250 members and the Council of Five Hundred with 500 members.
Napoleon Bonaparte became First Consul after the coup of 18 Brumaire on the 9th of November 1799, a plot co-planned by members of the Directory itself. The Conservative Senate proclaimed him Emperor of the French on the 18th of May 1804, formally ending the republic.