>The proposed European Constitution went a long way to fix this
Uhh... what?
Firstly, it was rejected by more than just the French and the Dutch. Secondly, the reason it was rejected is precisely because, for lack of democratic process, it structurally favors this kind of authoritarian opacity.
The proposed constitution doesn't even begin to fix this; it is instead the very cause.
The Constitution was implemented anyway after it was rejected by voters, by passing an endless series of "amendments" to the existing treaties, a mechanism chosen specifically to give national governments an excuse to not do the referendums that their constitutions required.
The people didn't want the EU to reform.