I had to look up Jo-Di caliper. That is a different beast.
You have a spring gauge in French inches. Sometimes called a Douzieme Gauge.
A douzieme gauge, in a standard now very much unused, as far as I know, 
in GB, AU and the US.
It was used in the making of jewellery where ... as I described earlier, 
it has the jaws to measure for manufacture the small items like the 
parts of the gemstone settings on a ring.
That scale along the arm is to measure the length of the band on the 
ring you are making...or maybe the length of a brooch. That kind of thing.
Most of jewellery making is ring making.
So, in mm where I've done it for 40 plus years, all the dimensions for 
the setting on an average hand made ring will be in the range of the jaws.
Up to around 15 or 16mm.
The band of a ring for an average woman's ring ring will be about 55 - 
60mm, and for a gentleman about 60 - 65mm.
To use the right amount of gold to make the ring the right finger size, 
those dimensions are read on the arm of your gauge.
When I started I used a spring gauge in mm, which was our UK and AU 
standard, not French like yours.
The French ones were still available here in Melbourne, Australia new in 
the 1970's, but I was not trained in that standard.
I quickly put my spring gauge aside for that purpose back in the 1970s 
for a few pretty good reasons, and have used a dial vernier caliper and 
small steel rule since.
I still use the spring gauge occasionally to get into a piece of 
jewellery to measure where my dial caliper jaws cannot.

Cheers,
Peter
www.petermcbride.com