So, I stopped by the place that sold me the "semi-cured" rubber sound insulation to get a product reference. The dude wouldn't give me any info, only that he could get as much as I need, and ship it anywhere (welcome to France!).
But... He did spill the words "masse polymère"... And that was enough: I have cracked the case...
Check this out : http://www.texsa.com/index.asp?i=3&prod=14
Looks like they even have a US distributor.
Before finding this site, I translated a French site, which I might as well include here :
"Range of high density visco-elastic (without bitumin) synthetique membranes. Available with or without adhesive backing, permitting the direct application to different types of substrates.
Intended for acoustic insulation of inclined roofs, vertical walls (either periferal or internal), ducting, floors and ceilings.
With adhesive backing : Tecsound S 35/ 60/ 70/ 100 and Tecsound SY 50/ 70
Without adhesive backing : Tecsound 35/ 60/ 70/ 100
Also available :
A composite laminate including a layer of sound absorbing felt : Tecsound FT 40/ 75/ 55AL
A composite laminate including two layers of sound absorbing felt and one layer of visco-elastic synthetique membrane: Tecsound 2FT 45/ 80
Available in thicknesses from 1.8 to 24 mm"
How to short-circuit evolution: Enshrine mediocrity.