I don't think that that would work, divebuddy. We are in a dreadful situation here and facing covert attacks. We need a covert response IMHO. Reality is facing us. If someone could have killed (even rendered helpless) one of those attackers in Paris, lives would have been saved.
Yes, one can quote the nutters who slipped through the net of gun licensing, but this idea is considering the creation of a totally different force, allowed to carry guns in normal life - which would, I agree, need careful selection and monitoring, far more than involved in day-to-day licensing.
We are at war, just as certainly as we were at war in 1939. Different thinking is needed. I'm hugely sorry that this is the case. I'm a peaceable soul who worked for understanding between religions for years, face to face. We need to shoulder the burden and, as I said, the reality of the situation, sad as it is.