Giving a feedback on this topic, maybe this can help someone else.
After the reseting the module as per factory and reprogramming the transmitter, this was not enough. I had to reprogram the PATS also on the transmiter like we program a third key when we have the 2 original keys. Then, the fourth and last thing I did was entering the Tach mode and puting the settings to ON. Then we were finally able to start the car. I made a last modification to avoid the car shutting down when you open the door.
Hope this will help.
2007 Shelby GT BV5
1989 Fox Convertible GT BV5