It was approved by the people in a referendum on 28 September 1958, and officially promulgated on 4 October that year.
The Kingdom of France, under the Ancien Régime, was an absolute monarchy and lacked a formal constitution; the regime essentially relied on custom.
That said, certain rules known as the fundamental laws of the Kingdom were outside the power of the monarch to change without further consent.
For instance, Louis XIV tried by his will and testament to change the inheritance order, but the Parlement annulled it.
[1][2] On the other hand, the law was occasionally changed, as when the provisions of the Peace of Utrecht renouncing the claim of Louis XIV's grandson Philippe to inherit the throne of France were approved to allow him to inherit the throne of Spain.