During the Lynx Challenge (Defi Lynx) lapel pin promotion there were two lots of coffret / display case boxes manufactured. Both contained a number of lapel pins, never the complete set however. There was a set of 100 numbered boxes and another set of 250.

These coffrets were made out of wood and had felt/sponge padding on the inside. Each box had 'DEFI LYNX Atari' painted on the top cover in gold coloured paint. The rear of the box had its copy number printed in black in the bottom left corner.

Both variants included two of the 'Atari Lynx' pins and a selection of game pins.

Coffret from the 100 box set🕸

See detailed Defi Lynx '100' series Coffret Box Dimensions.

Coffret from the 250 box set🕸

Above image and information from http://oldiesconsoles.free.fr/ (English translation)

Above image and information from AtariAge Forums