Hey Guillaume,
The best way by far to train to solve the 4x4 edges is to solve slowly without a timer and count your number of moves. Try to minimize this number of moves as much as possible, and don't care about the time taken to do it. If you spend 15 minutes on one edges solve, that's absolutely fine!
Then once you have found a method that cannot get any shorter than you already have it, start turning it into a mindless routine. Meaning that you can do it without even thinking about it, allowing you to start looking ahead a bit. Just do slow solves with your method (still no timer) and get used to doing it over and over and over an over ad nauseum...
Then once you have your method turned into a mindless routine, start working on looking ahead harder and going FAST!! Edges is about finding the perfect slow-fast pace, but to get really really fast times (low sub-60) you need to go actually fast for the edges and not really slow-fast.
Try that and see how it works for you, that's the method I used to train edges and I think I average about 20-22 seconds for edges. I've gotten times around 16-17 on really good solves and upwards of 26-28 on my slower solves.
Hope this helps,
Chris