Making a gelatin-based and non-sticky "salmon"
I can't read French fluently (or quickly), so I missed any specifics there.
It looks like you probably already cooked your fruit puree? If not, you should. Various fruits contain enzymes that will actively break down the gelatin protein and prevent it from setting properly. This would typically leave a bitter taste. But this might not be your problem.
The other thing you can try is simply using more gelatin powder. 2.25 teaspoons will set about 2 cups of liquid to a fairly soft consistency. You can increase the amount of gelatin to get a firmer, non-sticky gelatin sheet.
I will occasionally make gelatin &quot;noodles&quot; for dessert by 1) hydrating roughly 1/4 cup of unflavored gelatin with 1/2 cup of water, 2) and melting the lump of gelatin in 2 cups of whatever flavored/sweetened liquid I like. I let it set in a non-stick baking dish, or just a Pyrex dish, and generally gave no issue removing the sheet from the pan or slicing it into noodles. The edges might stick, but generally once the seal is broken, the gelatin can be slowly, gently pulled off the bottom of the pan. It will stretch a bit without breaking.
That works out to nearly 4 times the amount of required gelatin. I haven't experimented with reducing that amount since it serves my purposes, but there is plenty of room to do so. The texture of this gelatin is very firm, but it will still melt in your mouth, if more slowly, and is not rubbery or chewy. It also is not the least bit sticky.