My guess is that it would work only if you defined the Fourth Republic loosely, ie. it had a different constitutional structure. Looking at Wikipedia (yes, yes, but this isn't very...partisan information) it was quite unstable. Lots of Government changes between it's establishment and the Fifth Republic. So, if the constitution increases the stability compared to OTL, especially if it increases it to the stability of the Fifth Republic, then it has quite a good chance of lasting to today, or beyond.