Bayrou will not be running with the UDF; some of the current UDFers will probably join the UMP while others will follow him. His new party is the MD (Democratic Movement).
There apparently already was a tiny Parti Democrate in France, so Bayrou's new party is the Mouvement Democrate.
Right, Bayrou is creating a Mouvement Démocrate, but when? Does he have the time to establish a new party before June 10? I figured that he would stick to the UDF for now and create the MD during the months after the legislatives.
Either way, whether it runs under the banner of the UDF or the MD, I feel that the center
might deny the UMP a majority in June (although the legislatives usually mirror the presidential results), in which case it would effectively decide who gets to form the government.