Basque Beret?

Two years ago I published a post on the German (Nazi) Panzer Beret, a helmet cover that strongly resembled a Basque beret.  

However, these "berets" were nothing like the very large diameter Basque beret the soldier pictured above wears. No specific details available regarding date, location or background.
In size it appears to be a beret of the Chasseurs Alpins, but in detail (manufacturing) it clearly is not.