No, the cour de cassation is not the equivalent of the supreme court in many ways.

* It doesn't judge the constitutionality of laws. That's the constitutional court.

* It doesn't judge cases related to complaints against the administration. That's for the council of state.

* Its precedents don't bind lower courts, who are free to rule differently.

* In France, judges are explicitly forbidden to write a judgement that seems to hold in a general manner (article 5 of the penal procedure code) - we have a much stricter separation between the legislative and judiciary. They always judge specific cases. This applies to the cour de cassation as well.

It's just not useful to try and compare the US and French legal systems. They're too different.