Hello again !
After 2 calls to Adobe support, and only one answer (???), the problem was still there. I eventually restored an old backup of my system, done 4 months ago, and recovered the possibility to access Adobe servers and check the license of my soft. I am still in updating the system now. Adobe was unable to help, so i had to figure it out myself.
"You want something to be done, you have to do it yourself !"
Bad experience !
Thanks again to Numo M for trying !
Best,
C.