I have found a story about a small basque hat. Ill publish a photograph of it and its wonderful emblem on its lining. When I have the inclination. Its from this school somehow. (The photograph above is probably not related to these facts)
http://www.ustaritz.fr/fr/jeunesse-sports-loisirs/enfance-jeunesse/enseignement/afmr-etcharry.html
http://www.lesocial.fr/forums/read.php?f=2&i=43097&t=42372
http://www.richardspens.com/?page=ref/glossary/A.htm