As I posted already, you have to know exactly what you have. The link above is useless to someone with a P or V model Darne. A P is similar to a Charlin in that the breech block isn't easily removed. The P grade was discontinued, along with Charlins, in 1965, but a few were produced as late as 1968. I suppose when the actions were gone, those models were gone.
1955 was a time of great upheaval for the gun makers around St. Etienne. Many companies went out of business, and the remains were purchased and used by those companies with deeper pockets.
To further confuse the issue, the Darne company also built Charlins alongside Charlin badged Darnes. Also, Fransisque Darne produced copies of the 1894 patent Darne R action sometimes have a button to release the barrels.
As far as I know, you are correct in stating that a gun with a button always has the barrels dismounted by depressing the button, and breaking the interference fit between the barrels and the action.
Best,
Ted