Seems the French Telecom and Free Telecom play the ping pong game. France Telecom says the physical line is Ok, and I tell Free Telecom the line is not OK and they see it too. According to this picture, the quiality is really really bad. If I have 15 minutes of connectivity without disconnects, I am lucky at the moment.
No chance in playing any online based game at all. Especially during this Week-End.

Issues have been fixed end of February - at last. Actually - when the temperatures got freezing, all of a sudden the connection was really nice. It didn't even take 4 or 5 days for the connection to be better after the big cold, it happened the first day. For me - this means the water is somwehere on an exposed place.
After contacting Free/France Telecom again, I explained them my suspicion, and they checked. As predicted, the cable connection from our physical line was under water (actually - really under water), That water was frozen, so it was easy for them to actually patch my line on another higher position, and making sure there is not water. Since then - no more connection issues (fingers crossed).