What Bayrou offers, I think, is not so much institutional reform (as far as I can make out, his proposals on institutions are to increase decentralisation at the same time as to increase presidential power over parliament!), as a reset of the party system. Voters are attracted by the idea of a non-extreme alternative to the two major parties, a third way. Personally, I think it's an illusion, another occurrence of the old French political chestnut known as l'ouverture, where the right or left in power is supposed to be ready to "open up" to the other side. It has never come to anything yet - unless it was in the coalition jockeying of the 4th Republic, which has in fact been brought up in connection with Bayrou... Who definitely says he'll split the existing majors up and form a government with the bits...

All this is far from the VIe Republic. I'm certainly in favour of a reduction of presidential power in France. It might sit well with Royal to be the one to offer that - elect me president, and I will scale down my own powers.