Welcome to the forum. The French stones are an interesting topic and the Blue or Purple stones in particular are still a bit of a mystery, as they were used as a backing stone for the yellow coticule and known ubiquitously as BBW Belgian Blue Waterstones.
It is the Coticules that garnered all the attention and the BBW was thought of as just a backing stone, glued to a coticule, though many old ones are naturally bonded. Much of the pre-war production of the “blue/French” never re-started for a variety of reasons and much of the hands on knowledge lost.
Today a blue slate stone is use as a backer that has no real honing properties. But some now believe, those old combo stones, especially the natural combination stone, were in fact a dual grit stones, both of which may have been high quality, the blue stone overlooked and a variety of the “French” stones.
So, many stones, that have been poo pooed as just BBWs may be some of the high grit French stones.
Your stone is of the size that were cut and commonly sold for razor use, under a variety of brands, though they may have been mined by just a few mines.
I have a couple of that size that produce a fine shaving edge and several others in varying dimensions that produce a range of edges. Like all natural stones the grit composition is totally random and can change wildly from one side to the other.
For more information you might want to look at the
Razor & Stone site, many of us are also members there, the site is dedicated more towards stones for razor use, and has an excellent library of natural stone photos and much on the Blue, French stones.
Also the work of Henk & Janneke Bos,
here is their website and their work “Grinding and Honing Information for Ship and Tool Lovers. Part 4 pages 47-49 cover the Blue and French stones.
If your stone will produce a cutting edge better than a hard black ark is debatable and only testing will tell. With these stones, the use of slurry can dictate results, so experimenting with thinning slurry may improve performance.
Hard ark stone performance can be improved by lapping, with loose silicone oxide, finished on high grit wet and dry and burnished with flat carbon steel tools or knives. If your stone is flat and smooth, burnishing can improve edge performance production of the Arks.
