Similarly, when Julius Caesar turned the republic into an empire, and was subsequently assassinated: it did not mean the empire reverted back to being a republic - rather that centuries of increasingly despotic emperors lay ahead.
Their last king wasn't killed by the French, but died in exile in England, and was one of three (or four) kings (Louis XVIII, Charles X, (arguably Henry V), and Louis Phillippe, who reigned between the First Empire (and consequently also after the First Republic) and the Second Republic (and consequently also before the Second Empire.)
Their last monarch was even later, and also wasn't killed by the French, but died in exile in England. The series of governments after the last monarch includes only the Third through Fifth Republics (and, depending on how you look at it, the Vichy regime between the Third and Fourth Republics.)
And IIRC there wasn't much substantive difference between the Third and Fourth Republic; the latter was basically a restoration of the former after France was freed from German occupation, not a change in governing philosophy by the French people, so you could argue that there were as few as two substantively different French systems of government after the last monarch was deposed.