It indeed is a Les Latneuses. I don't think there ever was a blue or slate backing. Many Les Latneuses have been, and are, sold with the "hybrid" side as a backing. The "hybrid" side was considered usable for rough sharpening, because it's so hard that you can put on considerable pressure for working a bit of damage out of the edge of a knife, chisel or plain blade. It was Gary Haywood who discovered the special qualities of this "hybrid" side for razor finishing.
The problem here is that the "regular" side of this Coticule is concave. This does have an influence on the shape of the razors bevel. As long as you use only that side for doing all the work start to finish, it would not matter. The bevel will be slightly convex, matching the curve of the hone. If you were to set the bevel on a flat stone, finishing on the concave surface will even have a small advantage, because it favors the very tip of the edge. In a manner of speaking, a concave hone does "Unicot" without the need for tape. The effect is the same.
But doing the opposite, namely: going for concave to flat, will not work well. The flat side is not able to make proper contact with the tip of a convex bevel, even if the convex is only very minor.
If you have another Coricule, my advice is to keep this one concave as is, and use it as aspecial finisher. Les Latneuses are brilliant finishers in their own right, and I believe that you are going to be very pleasantly surprised if you take a good flat bevel for 30 laps to the concave side with a very thin slurry and 30 more on water after that.
You can also use the hybrid side with a decent slurry to accomplish said "good flat bevel", and finish othe concave side. Doing it the other way round does not work, as you already experienced.
Best regards,
Bart.