ok i've now got my answer... 
as you can see on the screen, the participants are blocked (145 persons in the room and now all new participant is refused)
it's a pity because we spend hours calling resellers to ensure the packs would be registered in time.
this problem will certainly have the repercussion that we'll have to change to another solution, despite Connect pro is a very good product in my opinion.
so sad

With a negative balance of 2,480 minutes (50% beyond the minutes you purchased), you can't be surprised that people are being blocked. I'm impressed that there is an allowance to go beyond the alloted minutes.
As you can see the burst pack minutes can go very fast, as you seem to have used 2,000 minutes in the course of one day. They are intended to be a means of dealing with sessions that may go over your licenisng limts, not a solution to a licensing limit. If this is what sways you to another solution, then I expect you will find some other tool/feature that leads you to being frustrated and moving on from it as well. This can be a learning experience and way to ensure that you don't face this again in the future by implementing the correct licensing. I worry that this is a shortcomming of a reseller not clearly explaining how the burst pack minutes work, but I'll leave that concern between you and your reseller.
I still believe that you would be better suited with a webinar/seminar room. I use the two terms because Adobe will be chaning the names of them from seminar rooms to webinar rooms in the future. Since I don't resell in France, and I'm not going to get into pricing, I'll try to stick with generic numbers to help clarify why you should look at a seminar room with your reseller and start using that instead of a meeting room for sessions that may have more than 100 attendees. Let's say that burst pack minutes cost 100 of whatever currency you want to use (this is not an accurate price of burst pack minutes but a nice round number for illustration) for 5,000 minutes. As you have shown you can use up 5,000 minutes very quickly. Now a 500 seat seiminar room will cost you aprox 13-14 times as much as the burst pack minutes for a 12 month unlimited use license. So, we'll put the break even point for the seminar room at 1,400 (also not an accurate number, but used for simplicity). If you use 5,000 burst pack minutes over aprox 3 days, that means that a 500 seat seminar room would have cost you less at 42 days or about 8.5 business weeks (5 days so weekened are not included).
I would strongly urge you to look at purchasing a seminar room to meet this one problem that you are facing with Connect. No product will meet every need perfectly, but finding the best way to meet your need with a tool that is the best solution for you can be invaluable.
Just some food for thought, and best of luck with whatever you decide to move forward with.