LOL @ the idea that Chirac had any ideology or beliefs at any point in time.
Anyway, Balladur's political culture and governing style were a much better match for UDF than Chirac's.
Woah, I mean he's a flip flopper, but its still generally accepted that he went from incarnating the right-wing of the French Republican right (ok the conservative-dirigiste Right) to almost Blairite levels of Third Wayism. It seems more evolutionary opportunism given historical circumstances than having no ideas at all. Maybe that's what you meant... He wouldn't have won the 2002 2nd round with 82% had he stuck with his old views, more 60-40 with many of the Plural Left not endorsing him the way they did.
Considering Nicholas Sarkozy is a Balladuriste, I find it hard to believe someone like Bayrou could support their political clan, other than to please a bitter VGE. Bayrou eventually kept his ministerial post under Chirac too.