How Many Dynasties Have Ruled France?

I'm reading a bio of the Empess Eugenie by Desmond Stewart. In passing
he mentioned some consider the Bonapartes to be the fourth dynasty to
rule France.

Who are the others? Capet, Bourbon and Orleans?

Francois R. Velde...

In the 18th century, it was considered that the Capetians ("kings of the 3d
race") had followed the Merovingians and the Carolingians. That would make the
Bonapartes the 4th.

Gillian White...

What about the Merovingians and the Carolingians? Could they be the first
two? The third one might cover everyone descended from Hugh Capet - Bourbon,
Orleans, Valois etc.

Guy Stair Sainty...

I think it depends what you mean by "France". Until the later Valois Monarchy
a significant proprotion of what is now present day France was not strictly part
of the Kingdom itself.

Stan Brown...

The House of Orleans was part of the House of Bourbon. The latter,
arguably, was part of the House of Capet. But the Merovingians and
Carolingians were truly separate dynasties.