Only if you map French politics on to a broader European sphere can you say, for example, Jacques Delors was a Christian Democrat, or François Bayrou is a CD. Whereas Delors was a member of the PS, and Bayrou's entire career has been spent under the Gaulliste wing. Right-left, you choose.

It's perfectly reasonable for Bayrou to want to break free of the left-right divide, and play the "centre" and what endlessly comes up in French politics, (and never works), which is called l'ouverture, (=opening up to the other side) - which he is allowing to fly as a kite with talk of his choosing DSK as PM if elected. And, who knows, in the present state of disillusionment with the political world, he just might pull off an electoral coup.

Then the chickens would come home to roost. One, he'd need a parliamentary majority, when currently his small party relies on the UMP for its 30-or-so seats in the Assembly. Two, governments composed of right and left ministers would have difficulty holding together - in the past, l'ouverture has always meant token jobs for one side of the divide, real power for the other, and in this case Bayrou would certainly not be handing over any real power to the left. (DSK kite notwithstanding - that's just an easy way to look more "open").

I listened to Bayrou earlier this morning on France Inter. Asked clearly if he was saying the UDF was the pivotal centre point of French politics, he replied yes. And seemed in a hurry to move on, that point of view is so plainly hard to argue.