Haven't done it but I suspect you'll run into problems. The type of doors you describe are framed on all sides. You would have to remove the framing on one side of each to get French doors that both open, with no post in the middle. With pre-hung storm doors, it is that part of the frame that acts as a "stop" and contains the latch that holds the door in place when closed. Without it, these doors would have no way to stay closed. And you would need one door that is hinged on the left, while the other is hinged on the right.
I would expect other problems as well.

I just re-read your post and realized you might not be talking about pre-hung storm doors. If that is the case, you still have to deal with buying or producing some type of latches that will allow them to be closed and stay closed. If you don't want a post in the center of the doors (French doors don't have one), you'll have to latch one door to the floor and/or top frame, then latch the other door to the first one when closed. Simply latching the doors to each other will not keep them closed.